Dudeney's puzzles and perplexities in The Strand Magazine His columns entitled Perplexities ran monthly from May 1910 through June 1930, and had numbered problems. Here I call them X1, X2, ..., retaining the original numbering and the original problem titles. (X for perpleXity.) He also contributed several longer articles with (usually) unnumbered problems; for example, he presented special puzzles every year at Christmas time, from 1908 to 1929. These are given numbers like Z12.3 here, meaning the third puzzle in 1912. (Z for puZzle.) A notation like "36(08)779-787" means volume 36 (1908), pages 779--787. The Strand also published an American edition, one month later, with different paging; I use the British volume/page numbers here, unless the letters US appear. The symbol * stands for an algebra problem that I decline to specify further I have not indexed Dudeney's other (non-puzzle) contributions to Strand, but I might as well list them here: 13(97)50-55 "Dr. Bernard's Patient" (a short story); 45(13)388-392, "The Antiquity of Modern Inventions"; 47(14)91-95, "Jose Capablanca: The Latest Chess Genius"; 75(28)92-93, "Napoleon as a Chess Player". A short story by his wife, Alice Dudeney, appeared in 60(20)396-403, "The Legacy". A profile by Fenn Sherie, "The Puzzle King: An Interview With Henry E. Dudeney," appeared in 71(26)398-404 and mentioned several of his most famous puzzles, with solutions. (Except for the solution to P514, the classical probl\`eme des m\'enages, of which he says he "tried to worry that out for several months" without success until a method flashed into his mind while listening to a performance of `Siegfried'! He was later to discuss this problem on page 76 of Amusements in Mathematics.) (c) 2001 Donald E Knuth [but freely downloadable for personal use in research] -------------------------------------------------------------- +12(96)720-726 The Professor's Puzzles; solutions 13(97)106-109. [A condensed form of this article appeared in his book The Canterbury Puzzles, pages 81--88 and puzzles CP67--72 (of the first edition, 1907). The original article also contained P12 and P84 from the Weekly Dispatch, and one curious further puzzle that I haven't seen elsewhere: Z96.1 Six little niggers: Find a sequence of the 14 rows/cols/diags of 6x6 so that the elements of adjacent lines are simultaneous queen moves apart, having one common point. +35(08)339-344 Puzzles from Games Z08.1 The forsaken king: Start chess with all the white pieces but only the black king; white to move and mate in six Z08.2 The amazons: Start with queens on c1,d1,e1,f1,g1,h1,h2,h3; move three of them, leaving 11 squares unattacked Z08.3 Queens and bishop puzzle: Put bishop in a2; add four queens so that all squares are occupied or attached ("rather a tough nut") Z08.4 Ancient Chinese puzzle: white rooks on a6 and c6, white king on b6, black king on b8; white to play and mate moving each of the three pieces exactly once Z08.5 Four puzzles in one (by Sam Loyd): given positions of white pieces, put black king so as to have mate in 0, stalemate, mate in 1, etc Z08.6 The witches' dance (by Shinkman): black queens a3, b5, b7; white queens e4,f2,g8,h6; move one at a time in any order, never with two attacking; end with the white queens on left halfboard, black queens on right halfboard Z08.7 The knights puzzle: 14 knights can cover the chessboard and each other; how many suffice if only the unoccupied cells need be attacked? Z08.8 The rookery: Checkmate with 8 rooks confined to a 3x3 subboard till end Z08.9 Checkmate!: retrograde chess Z08.10 Thirty-six mates: Given the positions of 8 white pawns and 16 black pawns/pieces, place 8 white pieces so as to maximize the ways to mate in one Z08.X Setting the board: How many ways to put chessman into initial positions? Z08.11 Foxes and goose: Who wins in a checkers-like game? Z08.12 Four-in-line puzzle: Arrange 10 counters in five lines of 4, all ways Z08.13 The grasshopper's quadrille (by E Lucas): exchange 24 white with 24 black in 7x7, fewest moves (no diagonal moves or captures) Z08.14 Solitaire Muggins (by Sam Loyd): The maximum score at dominoes [he claims the solution 200 never before published, but he evidently forgot that he had published it in The Weekly Dispatch, 17 Feb 1901] Z08.15 Domino magic square: Arrange 18 dominoes in 6x6, summing to 21 in each row/col/diag Z08.16 Twenty-five-up (by Loyd): Analyze a game with rolling and turning dice Z08.17 Central solitaire: Find solution to peg solitaire in 19 moves Z08.18 Bachet's square: How many ways to put the court cards into 4x4 array with no two of same suit or rank in row/col/diag? Z08.19 The thirty-one puzzle: Analyze a Nim-like game +35(08)455-458 Solutions SZ08.1 he says the first two white moves must be e4 and Qg4 SZ08.2 he says the solution (c1,c2,d1,g2,g3,h1,h2,h3 is unique, and claims that there's no way to leave 12 unattacked when 8 queens are present SZ08.3 queens at c5,d3,e4,h8; possible uniqueness not discussed SZ08.4 Rd6 Kc8; Ka7 Kc7; Rac6 mate SZ08.5, SZ08.6, SZ08.7, SZ08.8, SZ08.9, SZ08.10 SZ08.X (8! 2! 2! 2!).(8! 2! 2! 2!).2 SZ08.11, SZ08.12, SZ08.13, SZ08.14, SZ08.15, SZ08.16, SZ08.17 SZ08.18 4!.4!.2, the factor 2 being omitted from Bachet editions SZ08.19 +35(08)580-584 [US663-667] Some Much-Discussed Puzzles (He talks about many old chestnuts, like the Josephus problem. "It is a curious fact that the answers always given to some of the best-known puzzles that appear in every little book of fireside recreations that has been published for the last fifty or a hundred years are either quite unsatisfactory or clearly wrong. Yet nobody ever seems to detect their faults.") Z08.20 The sheep fold: Double the size of pen that has 50 hurdles, by adding the fewest new hurdles Z08.21 The puzzle wall: Build shortest wall to separate four cottages from four mansions and a lake +35(08)696 [US 36(08)107] Solutions SZ08.20 SZ08.21 Swastika-like symmetry is inferior to an I-like configuration +36(08)581-585 Tales with Tangrams [see AM 169] +36(08)779-787 The World's Best Puzzles He mentions the 6-piece burr puzzle (calling it `the ancient "Chinese Cross Puzzle"') and Chinese Rings ('the ancient "Tiring Irons"), etc., and also gives a few problems for readers to solve: Z08.22 Ahmes' puzzle (more than 300 years old): Solve x + x/7 = 19 Z08.23 Papa's puzzle: center of gravity Z08.24 Alcuin's puzzle: 100=3m+2w+c/2, m+w+c=100, integers m,w,c>0 Z08.25 Tartaglia's measuring puzzle: (24,0,0,0)->(8,8,8,0) with measures of sizes (24,13,11,5) Z08.26 Bachet's weights: Four weights to weight 1, 2, ..., 40 Z08.27 Chinese ring puzzle: How many moves to remove seven "Tiring Irons"? Z08.28 Bachet's wine bins: Fewer bottles although the sum per side remains Z08.29 Kirkman's schoolgirls: 15 girls 3x5 on seven days, all pairs occur Z08.30 Chessboard cover: with 3 queens, a rook, and a bishop [He says the only known way to cover a chessboard with 4 queens and a knight was given in Strand, August 1907; he shows what he thinks is the only way to do it with three queens and two rooks, all pieces guarded] Z08.31 The hat-peg puzzle: Find four adjacent 5-queen coverings of 8x8, starting with all in a column, ending with no two attacking Z08.32 Three sheep puzzle: Like the 5 queens puzzle, but on a 4x4 board Z08.33 Railway puzzle (circa 1888, author unknown): Interchange two railway cars on a small siding Z08.34 The lost square: Explain the paradox of 5x5 dissected into 3x8 Z08.35 The mitre puzzle (1835 or earlier): Cut into four congruent parts Z08.36 Tait's counter puzzle (P. G. Tait, 1884): abababab00 -> aaaabbbb00 Z08.37 Leapfrog puzzle: aaaa0bbb -> bbb0aaaa Z08.38 Heart puzzle: Detach string and bead from a wooden heart Z08.39 Dovetailed joints: Explain how they can apparently be at right angles Z08.40 Tower of Hanoi (Lucas): How many moves? Z08.41 Newton's tree puzzle: He shows 9 points, 10 lines of 3; he asks for 11 points in 16 lines of 3 (Wilkinson), 16 points, 15 lines of 4 [Although ascribed to Newton, it's a special case of the theorem of Pappus] Z08.42 Get off the earth (Loyd): Explain which Chinaman disappears Z08.43 Chain puzzle (Loyd): Most economical way to mend a broken chain Z08.44 Spider and the fly: Shortest wall-to-wall route in a certain box Z08.45 Triangle and square: Dissect equilateral triangle into a square Z08.46 Catching the mice: Josephus-like puzzle, with large count +37(09)113-116 Solutions SZ08.22, SZ08.12, SZ08.24, SZ08.25, SZ08.26 SZ08.27 `To solve a seven-ring "Tiring Irons" takes 85 moves (taking off or putting on a ring being a move), or 64 moves if we drop or put on the first two rings in one move.' SZ08.28, SZ08.29 [with interesting symmetry], SZ08.30, SZ08.31 SZ08.32 states that there are 47 ways, but doesn't show them; AM310 shows them SZ08.33, SZ08.34, SZ08.35, SZ08.36, SZ08.37, SZ08.38, SZ08.39, SZ08.40, SZ08.44 SZ08.41 is not given [see P179 and P388] SZ08.42 "Mr Loyd has never, I believe, published his solution...", and Dudeney proceeds to explain it in great detail SZ08.43, SZ08.45, SZ08.46 +37(09)442-448 Mazes and How to Thread Them [see AM, pages 127--137] +38(09)82-87 The Best Puzzles With Coins Z09.1 Five pennies equidistant: Make each of five touch all the others Z09.2 Judging distances: Optical illusion Z09.3 Coin trivia: On which side of a penny is the date? Z09.4 Coin packing: How many pennies can surround another? Z09.5 Coin stacking: How many thruppences fit on half a crown? Z09.6 Elephant puzzle: Find an elephant on the old-style Victoria penny Z09.7 Cross puzzle: In 2+2+6+6+2+2, how many subsets are corners of square? Z09.8 Crossed puzzle: Remove six of those 20, leaving no such squares [is essentially Hoffmann's P6.27] Z09.9 Square puzzle: Put 20 coins in square array, same number in row/col/diag Z09.10 Magic coins: English coins in 3x3 making 15 shillings in row/col/diag Z09.11 Even amounts: How many ways to put 6 pennies in 8x8, all row/col even Z09.12 Pile problem: 1111111111111111 -> 4400000000000044, always pass over 4 Z09.13 Pile problem variation: End with ...4...444... Z09.14 Another variation: End with 0040400000040400 (always in twelve moves) Z09.15 Ten coin puzzle: Make 5 lines of 4, with 5 coins at top or bottom Z09.16 Sharp's puzzle: [see AM page 230] Z09.17 Plates and coins: cyclic 111111111111 -> ..2..2..2..2..2..2.. always passing over 2 as you circle the table; minimize distance traveled Z09.18 Eight engines puzzle: Rearrange certain sliding blocks keeping one fixed Z09.19 Eccentric deal: end with head,tail,head,tail,head,tail,head Z09.20 Eleven coins: Remove 5, add 4, leave 9 [just a trick of wording] Z09.21 Making change: How many ways to change a farthing, ha'penny, ...sov'rn? Z09.22 Giving change: A has 50+25, B has 100+3+2, C 10+10+5+2+1, B pays 34 to A [Equivalent to Hoffmann's 4.107] Z09.23 Broken coins: [See AM29] Z09.24 Five coin flips: What are odds of getting at least four heads or tails Z09.25 Four coins in a bag: Expected value when {20,20,20,1} equally likely Z09.26 Heap: A simple one-pile nim game Z09.27 Sixpence under tumbler: A physics trick Z09.28 Purse puzzle: Another trick of wording [The American edition of Strand, published a month later, omitted problems Z09.3, Z09.5, Z09.6, Z09.19, Z09.21, Z09.23, and Z09.25.] +38(09)240-242 Solutions SZ09.1, SZ09.2, SZ09.3, SZ09.4, SZ09.5 [only one!], SZ09.6, SZ09.7 says 19, but he missed two of side \sqrt5; Strens collection copy has Dudeney's correction in his own hand SZ09.8 Cover the following six: 00 x0 xx0000 000xx0 [is there a better way?] 00 0x 11101 SZ09.9 His solution 2111 [see TeXbook p335!]; he doesn't mention 01111 1121 11011 1112 11110 1211 10111 SZ09.10, SZ09.11, SZ09.12, SZ09.13, SZ09.14, SZ09.15, SZ09.16, SZ09.17, SZ09.18 SZ09.19, SZ09.20, SZ09.21, SZ09.22, SZ09.23, SZ09.24, SZ09.25, SZ09.26, SZ09.27 SZ09.28 +38(09)670-676 The Paradox Party [see AM, pages 137--141] +39(10)US528, a note by HED at the end of the "Curiosities" page: "In our next issue will start a monthly page of Puzzles for the entertainment of our readers." X0: The game of two rooks where you cannot pass any attacked square, cf P362 +39(10)628 [US668] "Perplexities", A Page of Puzzles X1 The motor-garage puzzle: Interchange pairs of four cars in an E-shape X2 A spelling puzzle: Place 9 letters in 3x3, maximize three-letter words in row/col/diag in either direction (up to 16 are theoretically possible) X3 A queer thing in money: * S0 +39(10)757 X4 The "T" card puzzle: How many sols a+b+c+d+e=c+f+g+h+i, {a,...,i}={1,...,9}? X5 The "Strand" square: Seven disjoint 7 queens solutions on 7x7 X6 A fair distribution: * S1 43 moves S2 GET, TEG, SUP, PUS, PAT, TAP, GAS, SAG, PIG, GIP, SET, TIS, AIA S3 +40(10)140 X7 The mouse-trap puzzle: Exchange two cards, then catch 21 mice cyclically X8 A letter "N" chess problem (Loyd): Pieces arrange in N shape; mate in two X9 A digital puzzle: ab x cde = fghi, a x bcde = fghi, {a,...,i}={1,...,9} S4, S5, S6 +40(10)278 X10 The grasshopper puzzle: cyclic aAAAAA0BBBBBb to bBBBBB0AAAAAa X11 Four-in-line puzzle: Ten points in 6x10 array, 5 lines of 4 X12 A word square: Permute the offdiagonal elements of given 6x6 to achieve one S7, S8 S9 nine solutions only, e.g. 12x483=5796, 4x1963=7852 +40(10)420 X13 The ten sheep: How many 2x5 Young tableaux? X14 A chess puzzle: White K and Q mate black K without moving the white K X15 Domestic economy: * S10 States that the n-counter generalization needs n^2+4n+2 moves S11 Claims that there are only two ways S12 PASTOR/ATTIRE/STUPID/TIPTOE/ORIOLE/REDEEM [Hoffmann's P5.10h in 1893] +40(10)563 X16 The Dutchmen's wives (found in Ladies Diary 1739): * X17 The tube railways: Hamilton path from A delaying visit to C X18 A little dissection puzzle: Dissect square+halfsquare into four congr parts S13 He states the general formula for n (a Catalan number), without proof S14, S15 +40(10)624 X19 Boys and girls: 00ABABABAB -> BBBBAAAA00, each step swaps X20 The traveller's puzzle: Count routes from NW to SE corner, all steps S or E X21 The mystic eleven: Min and max abcdefghi div by 11, when {a,...,i} are nine of {0,1,...,9} S16, S17, S18 +40(10)822-824 Christmas Puzzles X22 Wilson's queer relationship: His uncle was also his nephew X23 The eight diners: Derangements (each got the wrong hat) X24 Mr. Pankhurst's "Patience": Variant of Klondike with full knowledge [In X274 he says Bergholt later gave this the new name "King Albert"] X25 Mr. Waterson's chess ending: White wins in hopeless-looking position X26 Eight chess problems: Each with eight pieces in one file S19, S20, S21 +41(11)116-117 X27 The ten counters: Five-peg tower of Hanoi, with 10 disks in 31 moves X28 The twenty-one trees: In 12 lines of 5 X29 The banner puzzle: Dissect square into two squares, don't cut the lions X30 The zigzag puzzle: Restricted sliding blocks, get K in corner of 3x3 without him moving in the center S22, S23, S24, S25, S26 +41(11)235 X31 The three queens: They checkmate black king without leaving bottom row X32 The farmer's puzzle: * X33 The football players: * S27 Says 111 moves will do 20 disks S28 S29 One square is 4x4, the other 3x3 S30 +41(11)362 X34 The wassail bowl: Pouring from (12,0,0,0,0,0) to (0,0,0,4,4,4) with capacities (12,5,3,12,12,12) X35 A quaint chess ending: X36 The star puzzle: Tour of 8x8 from c5 to d4 in 14 straight strokes S31, S32, S33 +41(11)503 X37 The sixteen sheep: Choose 9 interior edges, enclose (6,6,4) X38 Mate in three moves: White has only a rook, Black only a pawn X39 A puzzle for card-players: Cover edges of K12 with 11 perfect matchings S34, S35, S36 +41(11)627 X40 The four frogs: They change places; diagram intentionally obscures it X41 A coin puzzle: Prepare an arrangement, then deal and get HTHTHT X42 Chessboard solitaire: Jumping 32 counters until only 2 remain S37, S38 S39 In his schedule all have each other player as partner once, opponent twice +41(11)746 X43 A railway muddle: Get long trains past each other X44 A critical chess position: Mate in three from desperate position X45 Dissecting a mitre: Dissect square minus wedge into square X46 A perplexing distribution: One hundred coins make 19x19 pence in diff ways S40, S41, S42 +42(11)108 X47 A puzzle for motorists: Connect 8 sources to 8 sinks without crossing X48 The four digits: Represent 100 with four 1s, four 2s, ... X49 A puzzle with pawns: No three in line on 8x8, occupying d4 and e5 X50 A deal in apples: * S43, S44, S45, S46 +42(11)225 X51 A new counter puzzle: Interchange two pairs of bishops on 5x4 board, never letting opposing bishops attack X52 A veneer puzzle: Pack 4 L-tetrominoes and 4 Z-pentominoes into 6x6 X53 The honest dairyman: Pouring from A to B, then B to A, then A to B gives what mixtures? S47, S48, S49, S50 +42(11)348 X54 A new match puzzle: 18 matches can enclose 4- or 5-sided spaces of relative areas 3:1 X55 A tennis tournament: Three rounds of 4 couples, nobody playing twice with or against another X56 The Twickenham puzzle: abcdeABCDE0 -> CDeaEbAcBd0 on 11-cycle, lowercase move left, UPPERcase move right, can't jump your own case X57 Casting the die: Odds of getting exactly one 1 in four throws S51, S52, S53 +42(11)477 X58 The four stars: Cut 6x6 into 4 congruent parts, resp containing a6,c2,d2,e2 X59 Odds and evens game: Start with 15 beans, alternately take {1,2,3} until empty; then the player who has taken an odd number wins; generalize X60 Card triangles: Analyze a+b+c+d=d+e+f+g=g+h+i+a, {a,...,i}={1,...,9} X61 A domestic tragedy: Rebus, "A small underfed cat..." S54 [Non-rigidity makes many more solutions possible than he gives, and tends to "cook" all such match puzzles] S55 {AdBe,DaEb},{AeDb,EaBd},{AbEd,BaDe}; he states that 8 couples can similarly play a 7-day tournament [this is X985 below] S56, S57 +42(11)597 X62 A dungeon puzzle: Rook path starting at e1, maximum turnings X63 Mate in two: "A pretty little problem by Dr. Gold" X64 Mrs. Timpkins's age: * X65 The cone puzzle: Maximum volume of cylinder contained in a given cone S58 S59 "The general solution is two complex and length for this page" S60 S61 +42(11)786-788 Christmas Puzzles X66 The station-master's little poser: Too-too-too-too-too-too X67 London and York: Trick of words X68 A pavement puzzle: * X69 The tea-service puzzle: 5-puzzle to transform a0b to a0c in fewest moves aac aab X70 The post-office clerk's dilemma: * X71 The fifty puzzle: What three of {3,6,9,12,15,19,21,25,27,30} add to 50? X72 The labourer's question: * [7w=3i, w+i=365] X73 A new motor-car puzzle: Hamiltonian path in certain 12-vertex network S62 e1 to b1 in 57 moves S63, S64 S65 1/3 the altitude +43(12)116 X74 The nine circles: Pass through in four straight strokes X75 A new money puzzle: Smallest mult of farthings in L s d, using {1,...,9} X76 Mating ten kings at once: He cites a 1909 claim of nine X77 Buying chocolate: * S66, S67, S68, S69, S70, S71, S72, S73 +43(12)228 X78 The domino frame puzzle: Place 28 dominoes in 15x15 frame, all side sums 44 X79 The cardboard box: * [ab=120, bc=96, ac=80] X80 Playing for counters: * X81 Mate in two moves: (by Meredith) S74 Must use the width of the circles S75, S76, S77 +43(12)357 X82 The ten prisoners: Maximize evens in rows/cols/alldiags X83 A printer's error: a^b c^d = abcd X84 A chess puzzle: Put white R,R,N so that black K at d5 in check, can't move S78 Many different solutions; he doesn't discuss 42, 43 as alternative sums S79, S80 S81 A triple queen sacrifice (Black has three ways to take it, all lose) +43(12)478 X85 The crowded chessboard: Superpose sols to 8 queens, 8 rooks, 14 bishops, and 21(!) knights X86 A rebus motto: X87 The peal of bells: Ham cyc of 4! perms by adj xchs, no end thrice in row S82, S83, S84 +43(12)597 X88 The exchange puzzle: Achieve given perm by swapping adj pieces of opp color X89 The trusses of hay: Find {a,b,c,d,e} given the ten sums {a+b,a+c,...,d+e} X90 The stop-watch: Three hands nearly equidistant, with variation S85, S86 S87 states that solutions exist for any number of bells +43(12)718 X91 Inspecting a mine: Chinese postman on 4x5 grid X92 The letter block puzzle: 8-puzzle GEF/HCB/D0A -> ABC/DEF/GH0, fewest moves X93 A chain puzzle: Cheapest way to join up nine pieces of chain S88 sketches a proof that 17 moves is minimum S89 S90 +44(12)110 X94 Right and left puzzle: Fewest exchanges to achieve a given perm X95 Chinese money: * X96 The wizard's cats: 10 given points to be separated by three circles S91, S92 S93 He breaks up two short pieces +44(12)238 X97 Stepping-stones: Land twice on opposite shore, use each stone equally often X98 Concerning wheels: Part of train is always moving backwards X99 Simple multiplication: ab...z x 3 = b...za x 2, and a=3 S94, S95, S96 +44(12)350 X100 St. George and the dragon: Ham knight path on 7x7 from d4 to b2 X101 An easy square puzzle: Make square from 5 triangles of sides 1, 2, sqrt5 X102 The Union Jack: Draw as much as possible of this fig with continuous line [I mean, find the largest Eulerian subgraph; equiv to Chinese postman] S97, S98, S99 +44(12)478 X103 The honeycomb puzzle: Hamiltonian path to spell a familiar proverb X104 A shopping perplexity: * X105 A wonderful village: Tricky wording S100, S101, S102 +44(12)592 X106 The four knights' tours: Divide 8x8 into four congruent parts, each part admitting a Hamiltonian cycle X107 Torpedo practice: 16 points, sink as many as poss always passing under 3 X108 The four sons: Divide 3/4 of square into four same-shape parts each adjacent to the center S103, S104, S105 +44(12)774 S106, S107, S108 +44(12)796-798 A Set of Nutcrackers Z12.1 Queer relationships: A man married the sister of his widow... Z12.2 A legal difficulty: A man wills 2/3 or unborn child if a boy... Z12.3 An arithmetical question: * Z12.4 The doctor's query: Mixing liquids Z12.5 The new partner: * Z12.6 Elementary arithmetic: What number is a multiple of all numbers Z12.7 The nine almonds: Peg solitaire with diagonals Z12.8 A weighing puzzle: Divide 20 into 2+2+...+2 with weights 5 and 9 Z12.9 A fascinating puzzle-game: Odds and evens [X59] starting with 27, and with moves {1,2,3,4} +45(13)113 Perplexities. With Some Easy Puzzles for Beginners X109 A cutting-out puzzle: Dissect 1x5 into sqrt5 x sqrt5, four pieces X110 A new match mystery: Miser\'e Nim X111 The twelve mince-pies: 12 points in 7 lines of 4 [The next are designated "Easy Puzzles"] X112 Matches puzzle: Support matchbox with three matches, their heads untouched X113 The box of sweets: * X114 Anagrams: X115 Missing words: All anagrams of each other X116 Digits and squares: abc = def/2 = ghi/3, {a,...,i}={1,...,9} +45(13)118 Solutions to the Puzzles and Problems in Our Last Number SZ12.1, SZ12.2, SZ12.3, SZ12.4, SZ12.5 SZ12.6 "The product obtained by multiplying together all numbers!" SZ12.7, SZ12.8, SZ12.9 +45(13)238 X117 Reaping the corn: * X118 The six sheep-pens: Enclose 6 fields of equal size with 12 hurdles X119 The junior clerks' puzzle: * X120 A charade: Like CHAR-ADE X121 The mouse and the corn: Trick of wording X122 A word square: 5x5 S109, S110, S111, S112, S113, S114, S115, S116 +45(13)344 X123 Crossing the river: Officer and 357 soldiers X124 A patchwork puzzle: Make 13x13 from 12x12 and 5x5, maintaining the grid X125 An enigma: X126 A charade: X127 Flies on window-panes: 9x9 queens, six agree with another solution S117, S118, S119, S120, S121, S122 +45(13)478 X128 The reverse-way puzzle: 012345 -> 0654321 on a cycle X129 Simple division: 701 mod x = 1059 mod x = 1417 mod x = 2312 mod x X130 The Nihilists: * X131 The seven pigs: Separate them by three straight lines X132 A paradox: Four men all play and all gain money X133 A charade: S123, S124, S125, S126, S127 +45(13)598 X134 Round the coast: 8-letter word with pattern abcdedfb X135 The magic hexagon: {1,...,19} in 12 lines of 3 all make 23 X136 The two candles: * X137 Queer arithmetic: Trick of wording and roman numerals X138 Drawing a spiral: Approximately, using a compass X139 A charade: S128 [27 moves is far from best possible; the optimum is not clear] S129 [A better way will be discussed in S682 below] S130, S131, S132, S133 +45(13)710 X140 The forty-nine stars: Hit them all in 12 straight connected strokes X141 New measuring puzzle: (10,10,00) -> (x,14-x,3,3), capacities (10,10,5,4) X142 The nest of rectangles: How many in an n x n grid? X143 Curious numbers: x+1=y^2, 2x+1 = z^2 X144 A word square: 6x6 X145 The miners' holiday: * S134, S135, S136, S137, S138, S139 +46(13)110 X146 Water, gas, and electricity: Connect A,B,C to W,G,E; no pipes cross X147 An old three-line puzzle: Trickery (cheating) needed here too X148 Curtailment: Word loses its first and last letters X149 Find Ada's surname: * S140, S141, S142, S143, S144, S145 +46(13)221 X150 A plantation puzzle: 10 points in 5 lines of 4, in 7x7 minus a4 d7 g4 g7 X151 A family party: How can 1 grandfather + ... be only seven people? X152 The eighteen dominoes: Make magic square summing to 18 in row/col/diag X153 A charitable bequest: * X154 A word square: 5x5 S146, S147, S148, S149 +46(13)352 X155 The six frogs: (Or n frogs) Like X128 but not cyclic X156 The motor-bicycle race: * X157 The dissected circle: Fewest connected strokes, can trace more than once X158 The cyclists' feast: * X159 Their ages: * S150, S151, S152, S153, S154 +46(13)472 X160 The barrels of honey: * X161 Painting the lamp-posts: * X162 The lunatic stamp-licker: [A weird problem] X163 The joiner's problem: Dissect inverse (convex) mitre into square S155 21 moves [thus 6 better than his solution to the less constrained X128] S156, S157, S158, S159 +46(13)600 X164 The queen's journey: Max Euclidean dist from d1 in five noncrossing moves X165 The family ages: * X166 The fatal well: * X167 The educated frogs: 0AAABBB -> BBBAAA0, jumping by {0,1,2} X168 The germ puzzle: Dissect into two congruent parts with one cut S160, S161, S162, S163 +46(13)796-798 Christmas Eve at Hollibury Hall. A Record of Some Easy Puzzles Z13.1 Aunt Nancy's box: Concealed words in British Railway stops Z13.2 The motor-car fare: * Z13.3 The three squares: Enclose 3 equal squares with edges {2,2,2,2,1,1,1,1} Z13.4 Cats and dogs: Interchange two pairs of markers on a certain network Z13.5 Cutting the pudding: Cut into two congruent parts without hitting plums Z13.6 The nine circles: * Z13.7 The thirty-three pearls: * Z13.8 The hydroplane puzzle: * Z13.9 The chessboard puzzle: Assemble .CUT.THY.LIFE. into 8x8 Z13.10 The great scramble: * S164, S165, S166, S167, S168 +47(14)112-113 X169 The four postage-stamps: How many ways to put a tetromino in 3x4 box? X170 The Christmas-boxes: [A reprise of X46] X171 The twelve pennies: 11111111111 -> 222222000000 always passing over two X172 Mother and daughter: * X173 An angling pastime: Buried fish words X174 An enigma: X175 The four gates: * X176 The three sugar basins: * X177 Missing words: SZ13.1, SZ13.2, SZ13.3, SZ13.4, SZ13.5, SZ13.6, SZ13.7, SZ13.8, SZ13.9, SZ13.10 +47(14)233 X178 A dormitory puzzle: (a+b+c)/k=c+d+e=e+f+g=g+h+a, {a,...,h}=S, k={1,...,6} X179 Stealing the bell-ropes: * X180 The ten cards: A variant of kayles X181 Pocket money: Max coins unable to change 10 shillings X182 A word square: 5x5 S169, S170, S171, S172, S173, S174, S175, S176, S177 +47(14)358 X183 Placing halfpennies: Put unit circles into 3x5 box, |cent(k)-cent(k+1)|=2 X184 A teasing chess puzzle: Mate with two queens staying on diagonal X185 The two aeroplanes: * X186 An enigma: S178, S179, S180, S181, S182 +47(14)478 X187 A new bishop puzzle: Exchange 4 bishops on 5x4 [a disguised form of X51] X188 The Sabbath puzzle: If Christians, Jews, Turks travel around the world... X189 Adding the digits: Hokey coinage X190 Missing palindromes: "...between [NOON] and [EVE], when [BOB]..." S183, S184, S185, S186 +47(14)595 X191 The artillerymen's dilemma: A pyrimidal number also a square X192 Who was first?: A heard a gunshot, B saw the smoke, C saw the bullet hit X193 A calendar puzzle: Probability that a new century begins on Sunday X194 A trick with dice: Deduce a,b,c from ((2a+5)5+b)10+c S187 , S188, S189, S190 +47(14)707 X195 A new domino puzzle: 28-cycle with each quarter summing to 42 X196 To be solved mentally: * X197 The ten apples: Move one, then win at peg solitaire X198 A charade: X199 The Greek cross: To be assembled from four given pieces S191, S192, S193, S194 +48(14)95 X200 The tessellated tiles: Choose 16 of 20 4-colored tiles, make 4x4 square X201 The fly and the honey: * X202 Another tree-planting puzzle: 13 points in 9 lines of 4 X203 Excavations: Buried words X204 An alphabetical puzzle: English words ...a...e...i...o...u...y S195, S196, S197, S198, S199 +48(14)220 X205 Card magic squares: 3 magic 3x3s from {1,1,1,...,9,9,9}, diff sums not 15 X206 The new gun: Trick of words, the fencepost fallacy X207 A new cutting-out puzzle: Make square from a 29-cell shape X208 The three villages: * X209 A buried proverb: S200 [Surely there are many, many more solutions] S201, S202, S203, S204 +48(14)335 X210 A motor-car puzzle: Longest rook path from d8 with 15 turns, no line twice X211 The smugglers' wine: Distribute 7 quarts, 7 pints, 5 empties of each kind X212 The eighteen counters: Partition {1,1,1,2,2,3,3,5,5,10,10,10,20,20,20, 25,25,50} into three sets of six with the same sum X213 Catching the thief: * X214 Missing words: S205, S206, S207, S208, S209 +48(14)470 X215 The five regiments: Connect five sources to five sinks on 8x8 grid X216 The basket of potatoes: * X217 A chess puzzle: (by Frankenstein) Retract last move and mate in one X218 Concerning a cheque: * X219 Thrice beheaded: S210 Can go 70; if he had visited all points would have gone only 64 S211, S212, S213, S214 +48(14)589 X220 Exercising the spies: Fewest moves of 15-puzzle to make knight's string X221 The war-horse: * X222 Avoiding the mines: A broken line from bottom to top X223 The despatch-rider: * X224 A battle scene charade: S215, S216, S217, S218, S219 +48(14)777-779 Puzzles at a Village Inn Z14.1 The Louvain house: 1+...+(k-1)=(k+1)+...+n, 50 < n < 500 Z14.2 The red cross puzzle: Dissect Greek cross into two of half size Z14.3 The two turkeys: * Z14.4 Sinking the fishing boats: [Reprise of X140] Z14.5 Marching on city: 10 divisions all to arrive simultaneously Z14.6 Clock puzzle: * [The fencepost fallacy again: 6 seconds to strike 6,...] Z14.7 The bewitched watch: Clock hands switched S220, S221, S222, S223, S224 +49(15)111 X225 The fort garrisons: Make magic star from {16,18,20,22,24,26,28,28,32,36} X226 The iron chain: * X227 The humane Arab: X228 Charade: X229 New card magic squares: 52 cards into 4x4,6x6 magic squares (sums 36,37) X230 Longfellow's bees: * X231 Mate in three: (by Loyd) SZ14.1, SZ14.2, SZ14.3, SZ14.4, SZ14.5, SZ14.6, SZ14.7 +49(15)233 X232 Circling the squares: x(k)^2+x(k+1)^2=x(k+5)^2+x(k+6)^2, x(k)=x(k+10) X233 The Rajah's diamonds: * X234 Strange, though true: Fact about horse's legs X235 An historical puzzle: Arthur Connor's subversive verse S225, S226, S227, S228, S229, S230, S231 +49(15)345 X236 The strategic railways: 7 sliding blocks on 8-cycle, k <-> (k+1 or k+2) [is like X128, but with an odd number of frogs] X237 A military puzzle: 120 men in 12 rows of 11, equidistant from captain X238 The improvised draughts-board: 4+4+4+11+11+10+10+10 into 8x8 X239 Another street puzzle: [cf Z14.1] 1+3+...+(2k-1)=2+4+...+2n; also 2+4+...+2k = 1+3+...+2n-1 X240 Carrying the bags: 4 miles, 2 bags, old gardener, young boy S232, S233, S234, S235 +49(15)466 X241 War strategy: Chess position, Black to play, White to win X242 From the front: * X243 The Austrian pretzel: Most pieces with a single straight cut X244 Meeting the trains: * X245 Quaint arithmetic: MILD (Roman numerals) S236, S237, S238, S239, S240 +49(15)599 X246 The pirates' flag: Change 12 stripes to 10 X247 A cow's progeny: One per year starting at age 2; how many in 25 years? X248 The way to Tipperary: Shortest even number of steps X249 A remarkable plant: X250 A little two-mover: (by Loyd) S241, S242, S243, S244, S245 +49(15)712 0 0 0 0 0 0 X251 Nine men in a trench: Sliding blocks 0234567891 -> 1234567890 X252 A puzzle in billiards: * X253 Mutual accommodation: 5 queens, 5 rooks, 4 bishops, 10 knights on 5x5 [cf X85] X254 A word square: 5x5 X255 The price of apples: * S246 S247 Fibonacci numbers [but he doesn't know that F_1+...+F_n = F_{n+2}-1] S248, S249, S250 +50(15)113 X256 The 37 puzzle game: Add {1,2,3,4,5} until 37 (win) or more (lose); consecutive moves must differ X257 The five fences: Separate 16 points X258 The beheaded dignitary: X259 A military knot: Tangled sentences missing two words X260 The weighing-machine fraud: [Reprise of X89] S251, S252, S253, S254, S255 +50(15)210 X261 A star puzzle: Magic 6-star of {1,2,...,12} with sums 26 X262 A new domino puzzle: 8 dominoes in 4x4, even in each row/col/alldiag X263 A cryptic sign-board: A French pun X264 The coin and hole: What is largest coin that will pass thru a given hole? S256, S257, S258, S259, S260 +50(15)349 X265 Turks and Germans: Josephus 8-cycle with large increment X266 The digital century: 12+3-4+5+67+8+9=100; reduce to 3 signs X267 The cardboard box: How many hexominoes fold into a cubical box? X268 Missing words: S261, S262, S263, S264 +50(15)475 X269 The handcuffed prisoners: 9 men in triplets, 6 days, all 36 pairs adjacent X270 A new match puzzle: 3 equal squares with nine matches X271 An old chess puzzle: (by Marache) X272 Root extraction: (5+1+2)^3 = 512, (4+9+1+3)^3 = 4913; others? X273 A charade: S265, S266, S267, S268 +50(15)593 X274 "Strand" patience: Exchange two 9-card piles with 4 blank piles X275 Sawing the logs: * X276 The crescent and the star: Which has greater area? X277 More beheading: X278 An old two-mover: (by Loyd) S269 He has solved 21 prisoners in 15 days, "a hard nut" S270, S271 S272 There are three more: 5832, 17576, 19683 S273 +50(15)783-787 Unrecorded Cases. Can You Solve Them? Z15.1 The ruby brooch crime: 44 jewels -> 41 jewels but loops still each hold 8 Z15.2 The Brondesbury burglary: Three-letter word of rare letters: LYM Z15.3 Stealing the bell-ropes: How was it possible with only a penknife? Z15.4 The Pimlico murder: abc x de = acbde Z15.5 The stolen albums: 2a-d, 2a, and 2a+d all squares Z15.6 Who killed Rattenbury?: Z15.7 A strange disappearance: Z15.8 The trail of the smasher: A path of length 50 Z15.9 The shooting of Brooks: Visual pun S274 His best (not given) is 62 moves S275 S276 The areas are equal! S277, S278 +51(16)108-110 X279 The seven-pointed star: Magic {1,2,...,14} X280 Missing words: X281 Queen Victoria's acrostic: Said to be composed by her in 1856 X282 A curious chess puzzle: (by Barrett) X283 The Victoria cross: 8-puzzle, to rotate left (in 18 moves) SZ15.1, SZ15.2, SZ15.3, SZ15.4, SZ15.5, SZ15.8, SZ15.6, SZ15.7, SZ15.9 +51(16)168-169 X284 The Armenian maiden: Rook path a8 to g2 in 22 straight courses X285 The card pentagon: a+b+c=c+d+e=e+f+g=g+h+i=i+j+a, {a,...,j}={1,...,10} X286 The first double acrostic: X287 A charade: S279, S280, S281, S282, S283 +51(16)301 X288 A cunning answer: * X289 An enigma: X290 Oranges and apples: ABABABABAB00 -> 00AAAAABBBBB cyclically X291 A war drama: 3x3 word square and magic square X292 Freddy's pudding: Trick of wording S284, S285, S286, S287 +51(16)440 X293 The despatch-rider in Flanders: * X294 A familiar quotation: K I N I (Shakespeare) X295 The smuggled glycerine: * X296 A time puzzle: * X297 Anagrams: S288, S289, S290, S291, S292 +51(16)538 X298 A new leap-frog puzzle: 17-peg solitaire with diagonals, in 4 moves X299 Converting the Kaiser: Word ladder KAISER -> PORKER X300 An ingenious match puzzle: An outrageous mathematical pun X301 The missing letters: X302 Another zigzag puzzle: (by Shinkman) A sliding puzzle analogous to X30 S293, S294, S295, S296, S297 +51(16)641 X303 Reflected writing: How to do it easily X304 Academic courtesies: * X305 The twenty-two game: Like X256 but using {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4} X306 The wrong move: Chess problem analogous to X217, but with a new catch S298, S299, S300, S301, S302 +52(16)75 X307 The horse-shoe game: With two black and two white markers on 5 vertices X308 Find your enemy: * X309 The false scales: * X310 Mate with the pawn: (by Julien) X311 A relationship puzzle: This man's mother was my mother-in-law (trivial) S303, S304, S305, S306 +52(16)200 X312 Mine-sweeping: 14 straight courses from a4 to a4, at h2 after 7, kills 8x8 X313 Can it be done?: 32 chessmen all unable to move? X314 A trio of word squares: 5x5 with one word in common X315 Laying out shells: Sum of 4 consec triangles = square (eg 15+21+28+36=100) X316 An anagram: S307, S308, S309, S310, S311 +52(16)339 X317 Nine-letter puzzle: [A reprise of X2] X318 The amusements tax:* X319 The square, cross, and circle: From three aspects X320 The Nelson puzzle: Forcing a permutation X321 Numbered charade: (One-dimensional crossword puzzle) S312, S313, S314, S315, S316 +52(16)470 X322 Exchanging the knights: On 5x8, alternate moves, never attack an opponent X323 Donkey-riding: * X324 Domestic economy: * X325 A queer word: S317, S318, S319, S320, S321 +52(16)578 X326 The restaurant check: Exactly two subsets of {1,2,3,4,5,6,8,12,14,16,24} add up to x X327 The missing code word: *A*E*I**OU* X328 Two eight-pointed stars: A curious isomorphism between two hypergraphs X329 Mate in three: (by Loyd) S322 64 moves [is it minimum???] S323, S324, S325 +52(16)695-697 Posers at a Christmas Dinner Z16.1 Cryptic arrangement: A typographic rebus Z16.2 Threepence and twopence: * Z16.3 Arithmetic riddle: * Z16.4 Gardener's dilemma: Plant four shrubs equidistant from each other Z16.5 Drawing an oval: With one sweep of compass Z16.6 Drawing a square: With compasses only Z16.7 Circular field partition: Into four equal parts with equal-length fences Z16.8 Men walking and facing each other: Why didn't they get closer? Z16.9 Five Arab maxims: Concealed in a 6x6 square Z16.10 The 25-acre square: Debug an old puzzle Z16.11 Numerical riddle: Take half of five, remove one, get five [cf X137] Z16.12 Anagrams: On famous Englishman's names Z16.13 Another anagram: Make one word from NEW DOOR [cf Hoffmann's P5.2] Z16.14 Crowned kings: Why was there only one since the Conquest? Z16.15 Alphabetical riddles: Why is A like noon? ... Z16.16 The number 102840: Its hidden meaning Z16.17 Objects seen on a penny: For example, an animal (hare=hair) Z16.18 Sparkling puzzle: Remove one letter at a time S326, S327, S328, S329 +53(17)95-97 X330 The Russian motor-cyclists: * X331 The farmer's sons: Eight sons get same amount of land and trees X332 A reversed number: ba-9 = ab = 5(a+b) X333 The table-top and stools: Dissection with only six pieces X334 A knight's path: In 4x5, maximize the fixed points of its permutation X335 When did the dancing begin?: Clock hands changed places X336 The lost statesman: SZ16.1, SZ16.2, SZ16.3, SZ16.4 [tetrahedron], SZ16.5 [coil the paper first] SZ16.6, SZ16.7, SZ16.8, SZ16.9, SZ16.10, SZ16.11 [Roman numerals] SZ16.12, SZ16.13 [ONE WORD], SZ16.14, SZ16.15 SZ16.16 [One ought to wait for tea], SZ16.17, SZ16.18 +53(17)196 X337 The fly's tour: M\"obius strip X338 Counting the wounded: * X339 Drawing a straight line: Without a ruler X340 The two ships: * X341 The mutilated word: S330, S331, S332 S333 "Although every ellipse is an oval, every oval is not an ellipse" S334 Six fixed points, claimed to be maximum S335, S336 +53(17)311 X342 A tour on the icosahedron: Chinese postman X343 A mechanical paradox: Wheels and teeth X344 A pretty chess puzzle: (by Reichhelm) X345 Odd digits and even: 1+3+7+9/5 = 2+4+6+.8 S337, S338, S339, S340, S341 +53(17)415 X346 How far was it?: * X347 Shooting blackbirds: * X348 Getting the wine: Without a corkscrew X349 Playing for counters: * X350 A charade: S342, S343, S344, S345 +53(17)501 X351 A golf competition puzzle: Scheduling problem for 2n players on n links X352 The egg merchant's story: * X353 A new domino puzzle: Partition 28 into 7 foursomes, magic 3x3 minus center X354 The banker and the note: He finds & spends a note, later learns it's fake X355 A good two-mover: (by allender) S346, S347, S348, S349, S350 +53(17)607 X356 A "STRAND" puzzle: 6 solutions to 8 queens on 8x8 minus 2x2 center X357 The boat-race crew: Choose 4 L's and 4 R's from {4.L,5.R,2.[LR]} X358 Hurdles and sheep: Fewest unit lines to enclose an area of 10 or more X359 The three brothers: * X360 A word square: 5x5 given only the diagonal and another hint S351, S352, S353, S354, S355 +54(17)85 X361 A knight's move puzzle: 24-puzzle with jumping (not sliding) blocks X362 The three garden beds: * X363 The bun puzzle: Dissect three circles into four equal-area parts X364 More about hens: * [A new variation of the "hen-and-a-half" chestnut] X365 A cryptic word: S356, S357, S358, S359, S360 +54(17)181 X366 The word star puzzle: Five 4-letter words in a star configuration X367 Counting the huns: * X368 A pretty end-game: (by D'Orville) S361, S362, S363, S364, S365 +54(17)310 X369 A motto puzzle: Spell 25-letter proverb with king's path on 5x5 X370 Hoarded gold: * X371 A definition: High-falutin' description of a familiar household object X372 Those Russian cyclists again: * X373 A rebus: X374 A charade: S366, S367, S368 +54(17)415 X375 A new match puzzle: Odd number of matches to make 4x4 into 4+4+4+4 cells X376 Mrs. Wilson's family: * X377 A word square: 6x6 X378 An old chess puzzle: X379 An enigma: S369, S370, S371, S372, S373, S374 +54(17)407-410 War Tangrams +54(17)511 X380 Changing places: Knights and rooks on 4x4, analogous to X51 and X322 X381 A Dreamland clock: The minute hand moves backwards X382 The postwoman's puzzle: Chinese postman to circumnavigate 2x3 blocks X383 Sharing their pocket-money: * X384 A charade: S375, S376, S377, S378, S379 +54(17)621-624 Puzzles From a Secret Drawer. Some Easy Christmas Posers Z17.1 An elegant charade: Z17.2 Lady Anne's ribbon: * Z17.3 Stealing the bell-ropes: [A slight simplification of Z15.3] Z17.4 The two tinder-boxes: * Z17.5 Mrs. Hembrow's riddle: Z17.6 The bricklayer's task: * Z17.7 The carpet and the cup: Trick of wording Z17.8 Pictorial arithmetic: TENT-SHOE-POT+WIG+POST+HOE-TWIG Z17.9 The miller's toll: * Z17.10 Missionaries and cannibals: Only one of each could row Z17.11 The Sedgemoor festivities: * Z17.12 Word reversals: Z17.13 Weighing the fruit: * Z17.14 Peter Parker's pin puzzle: Nonattacking bishops on 8x8 S380, S381, S382, S383, S384 +55(18)81-82 X385 The German prisoner puzzle: A thinly disguised 8-puzzle, equivalent to 458/327/016 -> 123/456/078 in 26 moves X386 Sharing a bicycle: * X387 A cryptic language: Nightingale's song transcribed X388 The six queens: Must pass through all 14 row/col/diag on 6x6 X389 The three dice: Odds of throwing 7 or 13 = odds of throwing x or y X390 An arithmetical charade: X391 Buried geography: SZ17.1, SZ17.2, SZ17.3, SZ17.4, SZ17.5, SZ17.6, SZ17.7, SZ17.8, SZ17.9, SZ17.10 SZ17.11, SZ17.12, SZ17.13, SZ17.14 +55(18)183 5 1 1 5 X392 The "pill-boxes": 60002 -> 20006 sliding blocks 7 0 3 3 0 7 8 4 4 8 X393 A digital puzzle: abcdefgh x 6 = ABCDEFGHI, {1,...,9} each side X394 Large word squares: 7x7 X395 A pretty end-game: (by Cook) White to move and draw S385, S386, S387, S388, S389, S390, S391 +55(18)255 X396 The submarine net: Minimum cut X397 The ladder: * X398 The quarrelsome offspring: * X399 A rebus: S392, S393, S394, S395 +55(18)338 X400 The six submarines: Six wooden matches mutually touch [He also criticizes a suggested way to six coins to do so, cf Z09.1] X401 Digging a ditch: * X402 An alphabet puzzle: 28-letter sentence including {A,...,Z} X403 A charade: X404 A pretty finish: White mates in two S396, S397, S398, S399 +55(18)404 X405 The nine squares game: Dots and boxes X406 A card trick: * X407 More bicycling: Extend X386 to three people sharing a bike X408 Decapitations: S400, S401, S402, S403, S404 +55(18)488 X409 The domino swastika: (by Wilfrid Bailey!) X410 Building a word square: 7x7 given as anagrams X411 A charade: X412 The barrel of balsam: * S405, S406, S407, S408 +56(18)74 X413 The Siamese serpent: Draw as much as possible in one continuous line X414 Gidsby's geese: * X415 The traveller's puzzle: Fewest consec straight lines to cover 8x8, a4->a3 X416 A charade: X417 An enigma: S409, S410, S411, S412 +56(18)135 X418 The alien bomb-dodgers: 19 on each of 4 sides of a house X419 Word chains: ARMY -> NAVY with steps abcd -> cdef X420 The four fours: [He traces it to 1881] Three solutions for 89 X421 Find the word: S413, S414, S415, S416, S417 +56(18)228 X422 Economy in string: * X423 Missing words: X424 The six noughts: Choose six of fifteen given numbers, obtain the sum 1111 X425 An old three-mover: Mate in three with queen and bishop only X426 The printer's problem: {J,A,N,U,A,R,Y} \cup ... \cup {D,E,C,E,M,B,E,R} S418 S419 His solution ARMY MYTH THUS USER ERSE SEAL ALTO TOOL OLLA LANA NAVY breaks the rule that proper names [Erse] are not allowed; ARMY MYTH THAN ANNA NAVY is much better --- "ANNA" is not a proper name, it's an Indian coin S420, S421 +56(18)304 X427 The smugglers' wine: [Reprise of X211] X428 Simple division: A skeleton showing seven 7s X429 Two squares in one: Dissect two squares into one, don't cut the small one X430 An old enigma: X431 The digits and square: abc+def = ghi, {1,...,9} with extra constraint S422, S423, S424, S425, S426 +56(18)380 X432 Making a word square: 6x6 disguised by 32 disjoint knight moves X433 The postage-stamps puzzle: Chinese remainders * X434 Giving them names: Andrew is anagram of WANDER, etc. X435 The milk-and-water man: * [similar to but different from X53] X436 Missing words: S427, S428 S429 This construction nicely proves the theorem of Pythagoras S430, S431 +56(18)482-484 A Posy of Posers. The Puzzles of some Men in Blue Z18.1 Address of the letter: A typographic rebus Z18.2 The walking puzzle: * Z18.3 Five missing words: Z18.4 Hilman's puzzle: Find four disjoint paths summing to 20 Z18.5 Equal sum and product: using only 1s Z18.6 The Flanders Wheel: Another disguised 8-puzzle, rotate and reflect Z18.7 The precocious youngster: * Z18.8 Find the cat: Visual puzzle Z18.9 The farmer's seventeen horses: Legacy in proportions 1/2 : 1/3 : 1/9 Z18.10 The leg-raising puzzle: Trick of wording Z18.11 The false scales: * S432, S433, S434, S435, S436 +57(19)66-67 X437 A new match puzzle: * X438 Digital coincidences: a x b = def, a + b = fed X439 Making a pentagon: With a strip of paper and fingers only X440 A three-mover: (by Jespersen) X441 A word square: 5x5 SZ18.1, SZ18.2, SZ18.3, SZ18.4, SZ18.5, SZ18.6, SZ18.7, SZ18.8, SZ18.9 SZ18.10, SZ18.11 +57(19)162 X442 The four pennies: Geometry trick X443 A side-car problem: * X444 Lines and squares: Make exactly 100 squares with the fewest lines X445 A charade: X446 A cryptic message: Each word beheaded S437, S438, S439, S440, S441 +57(19)252-253 X447 Word circles: Put {A,E,I,N,O,P,R,S,T,U} in a circle, max words either dir X448 John and Jane: * X449 An unsolved enigma: X450 A teasing legacy: Largest addition sum in sterling, {0,1,...,9} S442, S443, S444, S445, S446 +57(19)346 X451 A cunning chess problem: (by Loyd) X452 The moving stairway: * X453 Is it very easy?: Trick X454 The two additions: {1,2,3,4,5,7,8,9} into equal 4-digit sums S447, S448 S449 (no solution yet; see below, following S459) S450 +57(19)446 X455 The ten barrels: min a+b+c+d=d+e+f+g=g+h+i+a, {a,...,j}={0,1,...,9} X456 The cow, goat, and goose: * X457 An old unicursal puzzle: Trick X458 Missing words: X459 A puzzling epitaph: S451, S452, S453, S454 +57(19)546 X460 The four draughtsmen: Reconstruct a grid that has been erased X461 Expanding words: One letter, then two, etc., always adding a new letter X462 The domino column: 28x2, each 3 consec 3 rows sum to (x,x) S455, S456, S457, S458, S459, S449 +58(19)100 X463 The nine queens: 9 queens on 11x11, all 9x9 subboards solve 9-queens prob X464 The man and the dog: * X465 Missing words: X466 Squares and digits: Square number ending with the most repeated digits S460, S461 S462 [The deltas (left minus right in each row) are 0, 1, -1, 0, 1, -1, ..., 0; since 28 is not a multiple of 3 you can't make a cycle] +58(19)200 X467 The six pennies: Placing them [an extension of X442] X468 Sir Walter Scott's enigma: X469 A crease problem: Fold page, SE corner touches W edge, min crease length X470 A money puzzle: (L6 13s) x 2 = L13 6s; find another S463, S464, S465, S466 +58(19)300 X471 Tessellated pavements: 29 square tiles per large square, fewest cuts X472 Hallam's enigma: X473 Mate in three: (by Cook) X474 The two fours: 64 with two 4s "It is a fascinating but bewildering puzzle" S467, S468, S469 S470 (L2 17s) x 6 = L17 2s +58(19)400 X475 What nationality?: Visual trick X476 Easy division: 7a...z = 7 x a...z7 X477 Making a pentagon: With each side 3 inches X478 Missing words: X479 A puzzle for accountants: Copying error loses L189 10s S471 S472 (no solution yet; see below, following X489) S473, S474 +58(19)500 X480 The knight and the calendar: When do all the adjacent dates sum to 100? X481 The profiteering grocer: * X482 The five squares: Trick of wording X483 A charade: X484 Buying cucumbers: * S475, S476, S477, S478, S479 +58(19)595 S480, S481, S482, S483, S484 +58(19)642-644 Simon in Puzzleland. A Christmas Fantasy Z19.1 Charade: Z19.2 Jack and Jill: * Z19.3 Mike's age: * Z19.4 The lost star: Find it in a patchwork quilt Z19.5 The five queens: Move two of them to cover all Z19.6 Odds and evens: Express numbers up to 100 using {1,3,5,7,9} once only; also do it with {0,2,4,6,8} once only Z19.7 The three table-cloths: The largest square they can cover without cutting +59(20)100 Solutions to Last Month's Puzzles and Problems [SZ19.1 appeared later, following S494 below] SZ19.2, SZ19.3, SZ19.4, SZ19.5, SZ19.6 +59(20)102 X485 A new Greek cross puzzle: Form a cross from four given pieces (trick) X486 Generous doles: * X487 Squaring the circle: (Approximately) X488 A mutilated anagram: Two 10-letter words containing {A,B,C,D,E,F,I} X489 Missing words: S472 and other "unsolved" enigmas [see WP pages 1--3] +59(20)204 X490 Folding postage-stamps: Folding a 2x4 array so that upper left is on top X491 A little train puzzle: * X492 Domino frames: With 24 dominoes, make three 5x5 frames X493 Snuffing doing: An unsolved trick puzzle he received in the mail X494 Missing words: S485, S486, S487, S488, S489 +59(20)304 X495 The asylum gambit: Reconstruct Black's 15th move, given the position after X496 Spending his tenpence: * X497 A rail problem: * X498 The king-maker: Expanding words S490, S491, S492 S493 (no solution yet; see below, following S503) S494, SZ19.1 +59(20)404 X499 A rook puzzle: 19-move rook path e6 to f6 on 10x10 X500 The seven applewomen: * trick X501 Hexagon to square: Dissection in six pieces X502 Letter pairs: 8-letter word with each letter occurring twice X503 Current coinage: a+b+c+d+e = c+f+g+h+i+j+k+l, 11 coins and one duplicate S495, S496, S497, S498 +59(20)504 X504 A motor-car journey: Count routes h8 to a1 avoiding c1,d4,e7 X505 The seven children: Odds that perm of {a,a,a,a,b,b,b} is b...b X506 A charade: X507 A day's sport: * X508 Mental arithmetic: Multiply 993 x 873 in a few seconds S499, S500 S501 [He seems to have forgotten his 5-piece dissection in P391=MP108] S502 REAPPEAR(!) [A reader later sends 10-letter ARRAIGNING, INTESTINES, p276] S503, S493 +59(20)535 S504, S505, S506, S507 S508 Use xy=(x-a)(y+a)+a(y-(x-a)): 873x993 = 872000+7x121 `["Perplexities," unavoidably held over, will appear next month.]' +60(20)88 X509 Punctuation: If is is not is ... X510 A cryptic monogram: Rebussy X511 The clerk's mistake: As he reinstated as herein stated ... X512 Changing the suit: Dissect spade to heart +60(20)184 X513 In memoriam: Chess puzzle with pieces in shape of a cross X514 Binks's good point: A word puzzle X515 A peg puzzle: On 7x7, move 3 of 10 pegs to make 5 lines of 4 X516 The flocks of sheep: * X517 ..... la guerre: APRES ... S509, S510, S511, S512 +60(20)276 X518 The damaged measure: Find Golomb ruler of length 33 with 8 marks ["A new puzzle that is interesting me very much at the time of writing, and I have not yet got quite to the bottom of the mystery of the general solution." He illustrates length 13 with 4 marks.] X519 The five vowels: Find a word with five consecutive vowels X520 The twenty-five-up puzzle: [Reprise of Z08.16] S513 S514 Asks if bOOKKEEper is only word with three successive doublets S515, S516, S517 +60(20)521 X521 Changing places: Rook and bishop on 4x4 [a sequel to X380, which he now says has a 15-move solution] X522 The repeated quartette: a x 365 = bcdebcde, maximize X523 The Victoria cross: Dissect Maltese cross to square X524 Another unsolved enigma: X525 A walking puzzle: * S518 1+3+1+9+2+7+2+6+2 = 33 = 1+1+1+1+6+6+6+6+5 [in X530 says at least 16 sols] S519, S520 +60(20)452 X526 Counting out the blacks: [Reprise of X265] X527 An enigma: X528 The horseshoe puzzle: Into seven parts with two cuts [an old chestnut] X529 A new street puzzle: 1+2+...+m = 2(1+2+...+n) S521 S522 35 moves ["I have not yet succeeded in finding a shorter solution"] S523 13 pieces [P369 had a similar but different cross allowing 5-piece answer; MP111 later gave a nice 7-piece dissection] S524, S525 +60(20)578-580 Christmas Puzzles at a Club Z20.1 The first losing-chess problem: White to play and lose [beautiful!] Z20.2 Setting the chessmen: Fewest swaps to make correct [beautiful] Z20.3 Odds and evens: Trick of wording Z20.4 Riding in the wind: * Z20.5 The seven circles: Compass construction Z20.6 Weighing the baby: * Z20.7 An alphabetical puzzle: Word containing {A,B,C,D,E,F,G,H,I} Z20.8 A typewriter cryptogram: Substitution cipher Z20.9 The six coins: English money Z20.10 A square with four pennies: If you have the right design on your pennies Z20.11 Alphabetical arithmetic: M x GIREATHNS = NEAGRTIHMS Z20.12 The lettered square: 6x6 with no repeats in row/col/diag, 7 symbols OK S526 [He discloses a curious law that demands further explanation!] S527, S528, S529 +61(21)91-92 X530 The six cottagers: Cyclic Golomb ruler of length 21 X531 A little shopping: * X532 Word-building: X533 Bottle and cork: * [Reprise of X113] X534 An enigma: [Also a note on X524] SZ20.1, SZ20.2, SZ20.3, SZ20.4, SZ20.5, SZ20.6, SZ20.7, SZ20.8, SZ20.9, SZ20.10 SZ20.11 NIGHTMARES SZ20.12 [Here he missed the 128 6-letter solutions, "diagonal latin squares" such as 012345 350214 541023 203451 124530 435102 which exist for all n>3; see D\'enes/Keedwell book, 6.1] +61(21)186 X535 The guarded chessboard: Can you cover and guard all with KQRRBBNN? X536 Dividing by 37: Find 49129308213 mod 37 "by inspection in a few seconds" X537 A Swastikaland map: Fewest colors, contains an intentional typo X538 A deal in eggs: * X539 Half the alphabet: 13-letter word, all letters different S530, S531, S532, S533, S534 +61(21)278 X540 A cube paradox: Passing one cube through another X541 Factory hands: * X542 The garden bed: Largest rectangle inside triangle excluding a given point X543 An unsolved enigma: X544 Reversing the digits: Solve 123456789x mod 1000000000 = 987654321 S535 (see also below, following S549) S536, S537, S538 S539 (see also below, following S549) +61(21)370 X545 Counter solitaire: Peg solitaire 00000000/xxxxxxxx/xxxxxxxx, no diag moves X546 The "Ark" reconstructed: Improvements on X524 X547 Word endings: Different ways to spell -tion X548 Playing for marbles: * [A reprise of X349] X549 The tube stairs: Chinese remainders S540, S541, S542 S543 (unsolved, but see note following S553) S544 +61(21)443 X550 The patchwork quilt: Decompose into two congruent parts X551 Two queer words: Transpose two letters and invert the meaning X552 A wages paradox: * X553 The queen and the chair: Another Victorian enigma with answer lost S545, S546, S547, S548, S549 S535 Solved if bishops can be on the same color S539 SUBORDINATELY (and AMBIDEXTROUSLY has 14) +61(21)558 X554 Paper folding: Make regular hexagon within a square X555 The four fours: Berwick's original version of the division skeleton X428 X556 The eight dominoes: In 4x4, no repeats in row/col/alldiag, max total pips X557 Odds and evens: An obvious way to transmit a bit S550, S551, S552 S553 (yet unsolved, see note following S562) S543 +62(21)94 X558 Railway routes: Count simple paths X559 Football results: Reconstruct scores from other tallies X560 The missing vowel: Epigrams that use only one of the five vowels X561 Army figures: * X562 Some anagrams: S554 S555 (corrected below, following S566) S556, S557 +62(21)190 X563 A wheel fallacy: Zeno-like paradox X564 A charade: [Reprise of X139] X565 Buying buns: * X566 Curious multiplication: The Rhind papyrus / Russian peasant method S558, S559 S560, S561, S562, S553 +62(21)286 X567 Squaring a star: Dissect 6-pointed star to square, 5 pieces (Escott) X568 Alphabetical sums: Actually an alphabetic division X569 Mr. Grindle's garden: Max area of quadrilateral with sides {7,8,9,10} X570 A new word chain: ADVERB, BASIC, CARD, DINE, ..., not nec in order S563, S564, S565, S566, S555 +62(21)378 X571 Buying tobacco: * X572 Another Victorian enigma: ["I will explain that ... my own solutions are in fact in print before the puzzles themselves are read by the public."] X573 Find the factors: 1234567890 = a x b, min |a-b| X574 A sad case of nur(s)itis: Decipher a line graph S567, S568, S569, S570 +62(21)470 X575 Fox and geese: [Reprise of Z08.11] [The game is also known as Wolf and sheep, Hare and hounds; see X590 below] X576 The two trains: * X577 "Simple" arithmetic: * X578 A charade: S571 S572 (see also below, following S583) S573, S574 +62(21)564-566 The Puzzle Cranks' Symposium Z21.1 Reductions in price: Geometric ratio Z21.2 Some word puzzles: Z21.3 The circulating motor car: * Z21.4 Railway shunting: ABCE -switch- E'FG => E'FG -switch- ABCE, engines E,E' Z21.5 Dissecting the moon: 2D crescent with 5 straight cuts, max pieces Z21.6 A Polish gamble: * Z21.7 Pawns against pieces: White two moves at a time but has only pawns Z21.8 Bruin goes shopping: Trick of words Z21.9 A curious legacy: * Z21.10 The circle and discs: Cover a unit circle with 5 disks radius r, min r S575, S576, S577, S578 +63(22)65-66 X579 Folding a pentagon: In a square sheet of paper X580 Exploring Mount Neverest: Traverse 100mi cycle, can carry 2 days' rations, walk 20mi/day [analogous to jeep on desert] X581 Timing the motor-car: * X582 A musical enigma: A note on four staves X583 A new alphabet puzzle: Sets of words containing 25 letters, all distinct SZ21.1, SZ21.2, SZ21.3 SZ21.4 (see also below, following S592] SZ21.5, SZ21.6, SZ21.7, SZ21.8, SZ21.9 SZ21.10 "A little less than 2/3" [the exact value is 1/phi=(sqrt5-1)/2=.61803] +63(22)164 X584 Three domino frames: In 4x4, six dominoes each, sums {6,12,18} [cf X492] X585 A clock puzzle: One hand is the square of the other, in (square) minutes X586 An amusing definition: Trick X587 Monkey and pulley: Satire on several classic chestnuts S579 S580 (see also below, following S592) S581 S582 "Don't be flat, be upright and be natural? "(see also below, after S587) S583 DUCKS FROG VEX JIB WALTZ NYMPH [See SGB p7: 5-letter words don't do it] S572 +63(22)278 X588 Cutting the cheese: Make regular hexagon by cutting a cube X589 A critical vote: * X590 Ancient "Fox and Geese": An old version with 17 geese on 3+3+7+7+7+3+3 X591 An old enigma: X592 An exceptional number: ab x c = de, {a,b,c,d,e}={k,k+1,k+2,k+3,k+4} S584 S585 (see also below, following S596) S586 S587 (see also below, following S596) S582 BACH [He missed it, tho knowing CPE's fugue on BACH] +63(22)372 X593 A curious end-game: (probably by Loyd) X594 The first "boomerang" puzzle: Chinese remainder acc to Nichomachus X595 The five cards: ab x cd - e = ffff, {a,b,c,d,e}={1,3,5,7,9} X596 A charade: S588, S589, S590, S591, S592, S580 SZ21.4 reduced to 14 moves +63(22)408 X597 The quinqueliteral: Five solutions to 5 queens on 5x5 in how many ways? X598 Missing words: X599 The four cubes: Solve 5^3+x^3=y^3+z^3 in integers X600 Beheadings and curtailings: X601 Distributing nuts: * S593, S594, S595, S596, S587, S585 +63(22)541 X602 Marking a tennis court: Nice application of Chinese postman X603 Two anagrams: [One of which reprises Z16.13] X604 Another old enigma: X605 The Mudbury War Memorial: * S597, S598 S599 5^3+315^3 = 248^3+252^3, and he constructs many more examples S600, S601 +64(22)48 X606 Digital squares: Eight equally spaced abc+def=ghi, {a,...,i}={1,...,9} X607 Letter multiplication: a x bcdef = edafbc, no 0 or 5 X608 Folding a pentagon: An extension of X439 X609 Missing words: Actually expanding words X610 A chess charade: S602, S603, S604, S605 +64(22)186 X611 Perpetual check: The shortest such chess game X612 Market transactions: * X613 Two little paradoxes: Why does a mirror reverse left/right, not top/bottom X614 An enigma: S606, S607, S608, S609, S610 +64(22)290 X615 A plantation puzzle: Separate 20 points of 6x6 with six straight fences X616 A word square: 6x6 X617 The new flag: Nonisomorphic digit triples (a,b,c) when (a,b,c)==(c,b,a) X618 Puzzles in a garden: * X619 A charade: S611, S612 S613 [His explanation is not really convincing] S614 +64(22)368 X620 The switch puzzle: 12-letter word reproduces itself vertically in 12 moves X621 A rising politician: Expanding words X622 An end-game: (by Bolton) Q and N versus Q and P X623 Find the coins: * S615, S616 S617 [Burnside's Lemma would give (1000+100)/2 immediately] S618, S619 +64(22)439 X624 Eight queens: Move 3 so that 11 cells are unattacked X625 The flock of geese: * X626 Twenty matches: 7 enclose area x, 13 enclose area 3x [not a good puzzle!] X627 The solitary seven: In a division skeleton X628 A rebus: No, it's actually three words that anagram each other S620, S621 S622 [See correction following SZ22.10 below] S623 +64(22)619-622 A Budget of Christmas Puzzles Z22.1 Find their ages: Trick of wording Z22.2 The donkey-cart journey: * [similar to X443] Z22.3 Imitative chess: Both players make the same moves until White mates Z22.4 The knight's century: Find a path that sums to 100 Z22.5 A charade: Z22.6 The stone pedestal: * Z22.7 The old Fifteen Puzzle: Trick to solve 15-puzzle with counters not blocks Z22.8 Cricket averages: Fallacy of statistics Z22.9 The rectangular field: * [with sexist remarks] Z22.10 Five figures from five pieces: Square, Greek cross, rectangle, diamond, and right triangle S624, S625, S626, S627, S628 +65(23)103-104 X629 An instructive position: Chess ending, Q and N versus Q X630 A poetical pot-pourri: Collage from lines of famous poems X631 Pat and the pig: Pat can run twice as fast, but always goes toward the pig X632 The keg of wine: * Mixing water and wine X633 Anagrams: X634 Adding their cubes: 407 = 4^3+0^3+7^3; find a case without 0 SZ22.1, SZ22.2, SZ22.3, SZ22.4, SZ22.5, SZ22.6 SZ22.7 Exchange 6 with 9 ["I have not looked for the shortest"] SZ22.8, SZ22.9, SZ22.10 S622 +65(23)208 X635 Twenty-six matches: Divide 6x6 into 2 same-shape pieces, one with d5 and f2, the other with b5 and c3 X636 Puzzling legacies: * [A typo will be corrected next month] X637 A magic-square trick: Quibbles of wording X638 A picture presentation: How many subsets of a 10-element set? [Trivial] X639 Missing words: S629, S630, S631, S632, S633 S634 1^3+5^3+3^3=153 [Hardy hated this puzzle!] +65(23)311-312 X640 The square table-top: Dissect 12x12+15x15+16x16 into 25x25 X641 A complete skeleton: (typo corrected later, see S641 following S648) X642 A word square: 5x5 X643 Baxter's dog: * [a companion to X464] X644 WRONG to RIGHT: Word ladder S635, S636, S637, S638, S639 +65(23)405 X645 The domino rectangle: 28 dominoes in 8x7 with row sums 21 and col sums 24 X646 Palindromic square numbers: 264^2=69696, but want an even number of digits X647 More expanding words: X648 The puzzle of the runners: * S640, S641, S642, S643 S644 (see also below, following S651) +65(23)538 X649 Drawing an oval: * (with string and pins) X650 Cricket scores: * X651 Block and pin puzzle: A companion to X313, 16 chessmen with <6 movable S645 S646 The smallest he knows is 836^2=698896 [and it is indeed smallest] S647, S648, S641 +65(23)627 X652 The garden path: * (compute its area, corner to corner) X653 Word multiplication: A x STEM = TEAMS, no zero X654 A new measuring puzzle: (inf,0,0)->(inf,8,x) or (inf,x,8), cap (inf,15,16) X655 Beheading: S649, S650 S651 (see also below, following S660) S644 WRONG,PRONG,PRONE,DRONE,DIONE,DION'S,SIONS,SIGNS,SIGHS,SIGHT,RIGHT [It has proper names and apostrophes, which he decided to allow because of the difficulty. My favorite solution without such liberties is WRONG,PRONG,PRONE,PHONE,SHONE,SHINE,WHINE,WHITE,WHITS,WAITS,WARTS,WARNS, BARNS,BURNS,BURNT,BURET,BERET,BEGET,BEGOT,BIGOT,BIGHT,RIGHT; there's a shorter one if you allow BRUNG.] +66(23)104 X656 The six-sided figure: Bordered by 9 matches X657 A cryptic sentence: A rebus X658 A running puzzle: * X659 An easy enigma: X660 Concerning a cube: * S652, S653 S654 Observes that one can get any multiple of the gcd of the two capacities S655 +66(23)126 X661 Disordered counters: Sliding blocks ijcfg abcde 0 0 -> 0 0 [when you straighten dehab fghij out his diagram] X662 Beeswax: Alphametic X663 My Lady's garden: * X664 The runner's refreshment: A terrible mathematical pun S656, S657, S658, S659, S660, S651 +66(23)289 X665 The nine bridges: Count Eulerian paths X666 Word building: Historical expanding-words puzzle X667 A fence problem: * X668 Alphabetical arithmetic: ab x c = de, fg - de = hi, {a,...,i}={1,...,9} X669 An enigma: (by Voltaire) S661 Achieves 40 moves [the obvious lower bound] S662, S663, S664 +66(23)380 X670 A domino star: chains of length 3,4,3,4,3,4,3,4 with 21 pips each X671 Crossing the ferry: 6 people, many forbidden combos X672 An old enigma: X673 Three nines: The largest number achievable with three nines X674 A charade: S665, S666, S667, S668, S669 +66(23)526 X675 Chess possibility: Show that a strange position could indeed occur X676 A legacy puzzle: * X677 Dividing the board: * X678 A charade: X679 A queer division: Trick of wording S670, S671, S672 S673 [Here he doesn't allow factorials of factorials, only of explicit digits, for (weak) reasons that he explained in the Weekly Dispatch 1900.02.04; but below in S924 he has evidently changed his mind] S674 +66(23)652-654 Christmas Problems. From the Proceedings of the Puzzle Club Z23.1 Pocket money: * Z23.2 The staircase race: Chinese remainders Z23.3 The cost of a suit: * Z23.4 Postage-stamps: a+b+c=c+d+e=e+f+g=g+h+a, min and max, given that {a,...,h} is a subset of {1,2,3,4,5,6,8,10,12,14,16,18,20,24,60,120,240,480} Z23.5 An old enigma: Z23.6 Making a chessboard: From an odd shape, cut it in two pieces Z23.7 Queer chess: Supply Black moves for mate in 4, if the White moves are f3, Kf2, Kg3, Kh4. Z23.8 The clown clock: Switch the hands and the time is correct Z23.9 The nine barrels: How many 3x3 Young tableaux? S675, S676, S677, S678, S679 +67(24)105-106 X680 A motor-ride puzzle: 16-move rook tour a8-a8, not using links d6-d7, d5-e5 [Note that the 16-move solution to AM320 does not satisfy this condition] X681 The queen and the knight: Probability that neither attacks the other X682 A common divisor: Solve 480608 mod x = 508811 mod x = 723217 mod x X683 A charade: X684 A digital difficulty: abcdefghij a mult of 1,...,18; {a,...,j}={0,...,9} SZ23.1, SZ23.2, SZ23.3 SZ23.4 (see also below, following S693) SZ23.5, SZ23.6, SZ23.7 e6, Qf6, Qf3ch, Be2mate, SZ23.8, SZ23.9 +67(24)196 X685 Changing places: Two knights, two bishops on either side, 8x8 [another in a series of similar puzzles, see X521] X686 Palindromic sentences: Form one from {A,A,A,A,E,E,G,G,I,I,L,N,N,R,R} X687 Missing words: S680 S681 4/9 S682 [He doesn't use Euclid's algorithm, he factors completely; perhaps he did this because most of his readers know only factoring?] S683 S684 (held over intentionally; see the solution following S693) +67(24)320 X688 Simple division: a...yz = 3 x za...y X689 The triangular plantation: Count noncollinear triples in a triangular grid X690 Dollars and cents: * X691 A puzzle with draughts: 10 in 8x8, 5 lines of 4, move six and make another X692 Threes and sevens: All digits 3 or 7, divisible by 21, sum of digits also X693 A word square: 5x5 S685, S686, S687 +67(24)424 X694 A general election: How many nonnegative solutions to w+x+y+z=615? X695 An enigma: X696 An epitaph (A.D. 1538): Family relations X697 For juveniles: * S688, S689, S690, S691, S692, S693, S684, SZ23.4 +67(24)516 X698 A reduced knight's tour: Bergholt found a 3x10, now find them all X699 Factorizing: Give two factors of 10^12+1 and 10^102+1 X700 Selling eggs: * X701 A rustic charade: X702 Apples and oranges: [Reprise of X265 and X526] S694, S695, S696, S697 +67(24)638 X703 The surveyor's problem: Chinese postman X704 A curious progression: In what familiar sequence is a_1+...+a_5=153? X705 The "antique" shop: Missing words X706 Two conundrums: S698 [He hints at the peculiar reversal symmetry in two of the cases] S699, S700, S701, S702 +68(24)97 X707 A prohibition poser: Measuring liquid (120,0,0,0) -> (x,1,1,118-x), cap (120,7,5,inf), cannot pour into the first component X708 Verbal arithmetic: Four alphametics, e.g., TWO x TWO = THREE X709 Scoring at billiards: * X710 The squares of veneer: Dissect 25x25 into 24x24 and 7x7 X711 A charade: S703, S704, S705, S706 +68(24)214 X712 An amusing chess puzzle: (by Morrow) don't allow the pawn to queen X713 A new word chain: BAG -> AGE -> GEM, etc. X714 Equal perimeters: Six integer-sided right triangles S707, S708, S709, S710, S711 +68(24)715 X715 Turning the die: [Identical to 25-up, thus another reprise of Z08.16] X716 Digits and primes: Prime numbers with smallest sum, using {1,...,9} X717 Striking out stars: Cover all of 7x7 by straight lines, from c6 to c6 X718 A charade: X719 The ADINCO puzzle: Wordplay X720 Paying the toll: Quibble S712 S713 (see also below, following S724) S714 +68(24)422 X721 Changing places: White/Black pieces all change, pawns only as necessary X722 Pickleminster to Quickville: * X723 The dishonest dairyman: Insert the letter I to make a sentence X724 Domino fractions: Discard doubles and blanks, then make three sets of five fractions that each sum to 10 S715, S716, S717, S718, S719, S720 +68(24)530 X725 Transferring the counters: 6-peg Hanoi tower, 15 disks X726 Prohibition again: Like X707 but allow pouring back into the barrel X727 A draughts problem: X728 The tramps and the biscuits: Like CP114, but nothing for dog on last day S721, S722, S723 S724 1/3+6/1+3/4+5/3+5/4 = 2/1+5/1+2/6+6/3+4/6 = 4/1+2/3+4/2+5/2+5/6 = 10 S713 +68(24)668-670 The Major's Christmas Puzzles Z24.1 John and Mary: * [a slight variation of X448] Z24.2 The damaged engine: * Z24.3 Buried fruits: Z24.4 A heptagon puzzle: a+b+c=c+d+e=...=m+n+a=19, {a,...,n}={1,...,14} Z24.5 A problem for surveyors: * Z24.6 A plantation puzzle: 10 points, 5 lines of 4, as close as possible to Newton's 9 points in 10 lines of 3 Z24.7 Missing words: Z24.8 Buying fruit: * Z24.9 The doctor's chess puzzle: Shortest legal game in which the White queen is not in line with or protected/attacked by anything else Z24.10 A word square: 6x6 Z24.11 The magisterial bench: Perms of {a,a,b,b,c,c,d,e,f,g}, no adj equalities Z24.12 The thirteen diamonds: 8x8 into 13 one-sided pieces, edges must match S725, S726 S727 [Amazing!] S728 +69(25)105-106 X729 A curious chess puzzle: (by Shinkman and Wurtzburg) X730 Word rings: ABCD -> CDEF -> EFAB [cf X419]; consider semantics too X731 Difference squares: 3x3 with a+b-c constant in row/col/diag X732 A charade: SZ24.1, SZ24.2, SZ24.3 SZ24.4 [He speaks as if his answer, (1,13,5,12,2,11,6,10,3,9,7,8,4,14), were unique; but (1,14,4,13,2,12,5,8,6,10,3,9,7,11) is another solution, and so is (1,14,4,13,2,10,7,9,3,11,5,8,6,12); I didn't continue looking. This problem, like X285, is related to generalizations of "graceful graphs" in which we want to label the vertices {1,...,n} so that the edge sums are distinct and form an interval] SZ24.5, SZ24.6, SZ24.7, SZ24.8 SZ24.9 e3 e6; h4 Qh4; Rh4 h5; Qf3 Kd8; Rh5 Rh5; Qh5 f6 SZ24.10, SZ24.11 SZ24.12 [There are actually four solutions. If we represent the given one as ABBBBBCC FFGGGGCC ADDEEBFC KK FJJ GAC AGHHIBFC IIK FJ GAC AGHIIJFC we can rotate inner part to IIH and/or change outer to FJ GAC.] AGKIIJFL IHH FB GAL AGKKJJFL EE FB DDAL MGGGGFFL MBBBBBAL MMMMLLLL MMMMLLLL +69(25)212 X733 Swastika magic square: 5x5, don't put primes or 1 into designated cells X734 A legacy puzzle: Twins not anticipated in the will X735 Triangles and square: Dissect two congr equilateral triangles to a square X736 A puzzle with cards: Construct an appropriate perm, ACE, TWO, ... [cf X41] X737 Missing letters: S729, S730, S731, S732 +69(25)294-295 X738 The cross-word clown: [Describes crossword puzzles as "A curious craze" from America "that will probably die as rapidly as it has sprung up"] X739 Dividing by eleven: How many perms of {1,...,9} are 9-digit nos div by 11? X740 A buried proverb: X741 The perplexed banker: Wants {1,...,1000} as subset sums of set X742 A charade: S733 S734 Due to summertime [daylight savings time], the firstborn was born later than the other S735, S736, S737 +69(25)424 X743 Novel cross-word puzzle: Letters given, clues in random order X744 Exploring the desert: 9 cars, no depots [and he neglects to say that they all should return home] X745 Cryptic verse: X746 Lamp signals: How many ways to place up to three pegs of three different colors into a 2x3 box, translations being considered equivalent X747 An old charade: S738 S739 [A typo is corrected below in X774] S740 S741 {1,2,4,...,256,489} is one way [and {1,1,...,1} is another of many] S742 +69(25)527 X748 Another cross-word curiosity: Each letter of alphabet used exactly once X749 A match-boarding order: Solve 297 = 8x+a(x-1)+x(x+2)+c(x-3), a+b+c=8 X750 An enigma: X751 Missing words: X752 Easy draughts: S743 S744 [An unsatisfactory answer; he implicitly forbids one car from waiting for another before returning home. Otherwise it is possible to go much further, using only 7 cars! I guess waiting is thought to be equivalent to "making a depot of petrol"] S745, S746, S747 +69(25)634 X753 Another cross-word variant: Gives lengths, not locations; fills in many X754 The fly and the motor-cars: * X755 Double-barrelled conundrums: [Ouch] X756 A little match puzzle: Remove some matches, leave four triangles S748, S749, S750, S751, S752 +70(25)107-108 X757 The British lion: Crossword puzzle in lion shape X758 De Morgan and another: * X759 The donjon keep window: A development of problem CP36, to divide a square window into eight subwindows whose sides are also equal X760 The two digits: When is ab = a op b? X761 Missing words: [very similar to X494] X762 A chess ending: (by Campbell) S753, S754, S755, S756 +70(25)202 X763 Easy draughts: X764 A rowing puzzle: * X765 Missing words: X766 Sheep stealing: * X767 Find the word: [Reprise of X488] S757, S758, S759 S760 (see also below, following S771) S761, S762 +70(25)320 X768 Cross-figure puzzle: Each cell to contain a single nonzero digit; sums are given as clues, in the four directions -, |, \, / X769 Two cyclists: * X770 A charade: X771 Another little match puzzle: Move three and enclose five cells S763, S764, S765, S766, S767 +70(25)423-424 X772 A fine chess ending: X773 Packing cigarettes: Tighter than 8 rows of 20 X774 Dividing by thirty-seven: [An extension of X739] X775 Missing words: X776 The sapphire brooch: [Reprise of Z15.1] S768, S769, S770, S771 S760 64 = sqrt(4^6); amazingly 71 = sqrt(1+7!) +70(25)524-525 X777 Les quadrilles: Classic problem but with no blanks allowed at outer edges X778 Squares and cubes: x^2-y^2 = m^3, x^3-y^3 = n^2 X779 Multiplication dates: 25 Jan 25 and 5 May 25 have Month x Day = Year X780 Odds and evens: A skeleton division with some parities specified X781 Buried animals: S772, S773, S774, S775, S776 +70(25)668-670 Z25.1 Twenty questions: Used to deduce a 6-digit number Z25.2 Cupid's arithmetic: Z25.3 A game with matches: Miser\'e Nim starting with {1,2,3,4,5} Z25.4 Age puzzle: a_1^2+...+a_9^2=(dad's age)^2, a's in arithmetic progression Z25.5 Counting the triangles: In pentagon+star Z25.6 A musical puzzle: God Save the King disguised with double-sharps etc. Z25.7 Word stairs: Z25.8 Three motor-cars: * Z25.9 An enigma: Z25.10 Dissecting the letter E: Cut in five pieces and make a square Z25.11 A charade: Z25.12 A chain puzzle: Extends X93, large and small links alternate S777, S778, S779 S780 (see also below, following S785) S781 +71(26)103-104 X782 A prime star: Made with 10 "primes" [he believes that 1 is "prime"] X783 The family ages: * X784 A tiny cross-word puzzle: 3x3 [joke] X785 The shortened word chain: Revisits X570, asking to make it short SZ25.1, SZ25.2, SZ25.3, SZ25.4, SZ25.5, SZ25.6, SZ25.7, SZ25.8, SZ25.9 SZ25.10, SZ25.11, SZ25.12 +71(26)208 X786 The treadmill: A chess problem by Reichhelm X787 Life's requirements: Missing words X788 The squares of veneer: A big improvement on S710 X789 Correcting a table: Errors of omission/commission in Ozanam's prime table S782, S783, S784, S785, S780 +71(26)312 X790 Easy draughts: (by Beattie) X791 An old charade: X792 Digital arithmetic: Another puzzle in pounds, shillings, pence X793 A new cross puzzle: Dissect Greek cross into smaller one and square X794 Domino sequences: With double nines S786, S787, S788, S789 +71(26)416 X795 A knight's path: step 1 on a1, step 4 on a2, ..., step 64 on a8 X796 Another skeleton: Division that specifies only one digit (a zero) X797 Octagon to square: Dissect one to the other X798 Queer division: x mod 45 =4, x mod 454 = 45, ..., x mod 45454 = 4545 X799 An old charade: S790, S791, S792, S793, S794 +71(26)521-522 X800 Ways of voting: Three items, each item is For or Against or Neither X801 An old enigma: X802 A deal in turkeys: * X803 A digital skeleton: Division in which the hidden digits are {1,...,9} X804 Card shuffling: What is the order of the Monge shuffle of 14 cards? S795, S796 S797 (see also below, following S818) S798, S799 +71(26)628 X805 Archery: Reach 100 with fewest elements of {16,17,23,24,39,40} X806 Digits and squares: abcde is a square, ab*de is a cube X807 Domino solitaire: Extend Z08.14 to allow building 4 ways from first double X808 Horses and bullocks: * S800, S801, S802, S803, S804 +72(26)103-104 X809 A carpet puzzle: Make a square carpet from 40x33 minus 8x3 X810 The pedestrian passenger: * X811 Naming his sons: Missing words X812 Cube differences: x^3-y^3=1234567 X813 Knight errantry: Chess puzzle (by Carpenter) X814 Palindromes: Beginning/ending with A, B, ..., Z, as many as possible S805, S806 S807 A conjectured optimum of 485 S808 +72(26)211-212 X815 The shortest draughts game: Twelve moves, no captures, White is then stuck X816 The barman's puzzle: * X817 The paper ribbon: * (find its approximate length, knowing its volume) X818 Sunrise and sunset: Missing words S809, S810, S811, S812, S813, S814 +72(26)315-316 X819 The entangled scissors: "The old scissors and string puzzle" X820 Geometrical progression: 1+a+a^2+...+a^n = x^2 X821 The puzzle of the iceman: Missing words ending -ICE X822 The dissected chessboard: "An ancient and familiar fallacy" that 8x8=5x13; use the same two pieces to prove that 64=63 X823 Maximum moves in chess: "In a possible (however improbable) position" S815, S816, S817, S818 S797 A nice 5-piece dissection +72(26)419 X824 Digital puzzle: abc divisible by (a+b+c)^2, {a,b,c} distinct X825 Subscription puzzle: * X826 An absolute skeleton: Division skeleton with not-too-nice restrictions X827 An old enigma: S819, S820, S821, S822 S823 His solution has 90 moves for White +72(26)526 X828 Another target puzzle: Cut {1,1,1,2,2,3,3,5,5,10,10,10,20,20,20,25,25,50} into three sets of six, each having the same sum [is equiv to X212!] X829 Curious square numbers: * X830 Moving counter puzzle: Halma on chessboard, swap 10 with 10, leaps only X831 Missing word puzzle: Each missing word used twice in each sentence X832 Magic fifteen puzzle: Starting with 14/15 swapped, go to magic square [AM403 was the same problem but without the swap; it has a nicer answer] S824 (corrected below, following S832) S825 S826 (see also below, following S832) S827 +72(26)664-666 Uncle Jasper's Puzzle Book Z26.1 Monkeys and nuts: Chinese remainder Z26.2 The keys and ring: Cut out of a single piece of cardboard Z26.3 The Arab's puzzle: abcd x efghi = acgefhibd, {a,...,i} = {1,...,9} Z26.4 Blowing out the candle: Through a cone Z26.5 A motoring puzzle: * Z26.6 Find the squares: x+100 = m^2, x+164 = n^2, x>0 Z26.7 My South American tour: A to Z in longest simple path [Interesting graph] Z26.8 The Spaniard's chess puzzle: Shortest game leading to White pawns on h2 h3 h4 h5 h6 h7 and kings on their original squares, no other pieces Z26.9 A juvenile poser: L to N trick [not great] Z26.10 Buying peaches: Z26.11 The Tower of Pisa: Sum a geometric series [bouncing ball] Z26.12 Ching's cutting-out puzzle: Fold a Greek cross, make one cut, get four pieces that yield a square S828, S829 S830 A simple impossibility proof S831, S832, S824, S826 +73(27)105-106 X833 Easy draughts: X834 Out and home: * X835 An old enigma: X836 Alphabet words: A five-syllable word represented by five letters X837 A tiny magic square: 3x3 using {1,2,3} in each row SZ26.1, SZ26.2 SZ26.3 6543 x 98271 = 642987153 SZ26.4, SZ26.5, SZ26.6 SZ26.7 There are longest paths leaving out any one of 11 vertices SZ26.8 (see also below, following S851) SZ26.9, SZ26.10, SZ26.11, SZ26.12 +73(27)210 X838 A curious end-game: X839 Word reversals and reflections: Handwritten word, same when rotated 180 X840 Blindness in bats: Simple statistics X841 Dissecting the letter E: In four pieces if you can turn them over S833, S834, S835 S836 XPDNC (expediency) S837 +73(27)305 X842 The shock: What is wrong with this story? X843 The eight knights magic: Eight paths {1,2,...,8}, row/col/diag sums all 36 X844 Table-top and stools: Loyd's 4-piece solution to X333=AM157 X845 Find the triangle: Sides and height are {x,x+1,x+2,x+3} X846 Eliza's surname: * (Logic puzzle, an extension of "Dutchmen's wives" S838 S839 "bung" S840, S841 +73(27)420 X847 Danger signal puzzle: Crossword with subsets only [cheap] X848 A queer number: A square when read forward, backward, and upside down X849 An old enigma: A E I O U X850 The motor-car maker's profit: * X851 Heptagon and square: A 10-piece dissection by Wotherspoon S842, S843, S844, S845, S846 +73(27)525-526 X852 The cancelled cheque: ab, cd, ef are squares, and so is abcdef/113 X853 The ambiguous clock: Both hands identical; when is time ambiguous? X854 A phonetic exercise: Extension of X836 X855 Securing the almond: A Nim-like game with real-number moves S847 S848 961, 169, 196 S849, S850 S851 (see also below, following S865) SZ26.8 reduced from 35 to 32 moves +73(27)630 X856 Luck in adjudications: Mate in 3 X857 Accommodating squares: abc = m^2, def = n^2, abcdef = p^2, no 0s X858 Making a square: From embellished cross 1+3+5+3+1 X859 The omnibus ride: * X860 A sequel to the iceman: Sequel to X821 S852, S853, S854, S855 +74(27)861 X861 Blocks and squares: a^2+x=b^2, b^2+x=c^2, c^2+x=d^2+4, minimum x X862 Sharing the apples: * X863 A charade: X864 The guarded chessboard: Sequel to Z08.3: 12 sols to 5-queens, 4 in common X865 The three drovers: * S856, S857, S858, S859, S860 +74(27)200 X866 Easy draughts problem: (by Muir) X867 The tank puzzle: * X868 Tremendous all: Missing words -TRE X869 A match puzzle: Hexagon -> two diamonds X870 Proportional representation: How many possible ballots? S861, S862, S863 S864 All but two are covered by c4 d8 g3 h7 S865 S851 Says that nine-piece solutions have been found, but he doesn't show them +74(27)318 X871 The Grand Lama's problem: Sequel to X58, make another such problem X872 New match puzzle: X873 Missing words: X874 Equal fractions: Like a/b=c/d=ef/ghi, {a,...,i}={1,...,9} X875 An enigma: S866, S867, S868, S869, S870 +74(27)417 X876 Conditional magic square: 5x5 with {1,3,...,25} in the central diamond X877 The conspirators' code: An alphametic X878 Boxes of cordite: Largest number not 15x+18y+20z in nonnegative integers X879 Two more queer words: A sequel to X551 S871, S872, S873 S874 He cheats with .2/1 = .6/3 = 97/485 S875 +74(27)521 X880 Curious cross-words: All words have the form ---IC X881 A queer position: How could both rooks infiltrate enemy territory? X882 A return journey: * X883 Drop letter puzzle: A Coleridge quote minus its vowels X884 The stopped clock: Hour hand = minute hand; second hand near 11 sec S876 S877 S878 S879 +74(27)670-672 A Batch of Easy Puzzles Z27.1 Two anagrams: Z27.2 Division of labour: [Reprise of X240] Z27.3 Fathers and sons: Relationships Z27.4 Hens and eggs: Hen-and-a-half again Z27.5 Where is it?: Trick [No W here] Z27.6 A match puzzle: Z27.7 The cyclist and the eggs: Trick of wording Z27.8 More magic numbers: [Reprise of X137] Z27.9 The Christmas presents: * Z27.10 An egg puzzle: * Z27.11 The square of soldiers: * Z27.12 The two D's: Rebus, horrible pun Z27.13 Clipping the coins: * S880 S881 (see also below, following SZ27.13) S882, S883, S884 +75(28)103-104 X885 Two domino squares: 10x10 and 6x6 frames, all 8 sides should have same sum X886 Varied spellings: For the long vowel A X887 The birth of Boadicea: * X888 Chess or Draughts: From the same position White mates in two / wins in two X889 Diminishing words: UNDESIRABLE, UNREALIZED, LAUNDRIES, ... SZ27.1, SZ27.2, SZ27.3, SZ27.4, SZ27.5, SZ27.6, SZ27.7, SZ27.8, SZ27.9 SZ27.10, SZ27.11, SZ27.12, SZ27.13, S881 +75(28)208 X890 A Monmouth tombstone: How many ways does it spell HERE LIES JOHN ... X891 An old enigma: X892 A triangle puzzle: Sides {x,x+1,x+2}, area divisible by 20 X893 Changed heads: Word play X894 The moving staircase: Sequel to X452 S885 S886 (see also below, following S904) S887, S888, S889 +75(28)296 X895 Eight motor-cars: 8-puzzle, 123/405/678 -> magic square X896 Another street puzzle: The perm 1,2,...,n -> 2,4,...,n,...,3,1 has the unique fixed point 181; what is n? X897 Missing words: X898 Easy draughts: X899 The year 1927: Belatedly, solve x^y - y^x = 1927 S890, S891, S892, S893, S894 +75(28)416 X900 The letter L: How many sols to a+b+c+d+e=e+f+g+h+i, {a,...,i}={1,...,9}? X901 Another age puzzle: * X902 Economic chess problems: (by Loyd) X903 A garden puzzle: What is largest quadrilateral area, sides {10,12,16,20}? X904 Words with one tail: DISTEND, PORTEND, ... S895, S896, S897, S898, S899 +75(28)522 X905 A framed knight's tour: Find a closed tour on 10x10 - 4x4 in center X906 A digital puzzle: 1234+1243+...+4321 [Bhaskara] X907 A hidden proverb: In king's tour of 6x6 X908 A leap year puzzle: When next will February have five Wednesdays? X909 Flooring figures: L1 4s 8d = 148 x 2 pence; L1 5s 0d = 150 x 2 pence; ... S900 (see also below, following S913) S901, S902, S903, S904, S886 +75(28)613 X910 An effervescent puzzle: Count perms of {E,F,F,E,R,V,E,S,C,E,S} with no EE X911 Water measurement: (inf,0,0) -> (inf,2,*) or (inf,*,2) or (inf,1,1), capacities (inf,7,11) [see X654] X912 Cremated animals: Word play X913 Summing the digits: 123456789+123456798+...+987654321 [cf X906] S905, S906, S907, S908, S909 +76(28)104 X914 Bishops and their sees: Move 14 from given position so that none attack X915 Letter figure puzzle: [not memorable] X916 Slim dominoes: Chains of lengths 7, 5, 4, 12 with equal sums [not great] X917 Football news: X918 Squaring the digits: abcdefghi = square, {1,...,9}, closest to 123456789 S910, S911, S912, S913, S900 +76(28)208 X919 The twenty-two bridges: Reprise of Euler X920 A solitaire puzzle: Peg solitaire from all-but-2 to only-2 X921 Finding a birthday: * X922 The five vowels: Longest case where XaY, XeY, XiY, XoY, XuY are all words S914, S915, S916, S917, S918 +76(28)312 X923 The king's march: How many ways from e1 to e8 in 8 moes? X924 Expressing 24: 24 = 22+2 = 3^3-3 = 8+8+8; other ways? X925 A new magic square: 3x3 with 4-digit numbers; digits are {9.1,9.2,9.3,9.4} X926 Hidden quotation: Change one letter in each word to restore it X927 The egg cabinet: * S919 S920 See also X934, reporting 20-move solutions by Moore S921, S922 +76(28)405 X928 Easy draughts: (by Lyman) X929 Squares and cubes: Sequel to X778: x^2+y^2 = m^3, x^3+y^3 = n^2 X930 An old enigma: A rebus X931 An old card trick: Once again, card spelling ACE, TWO [X736] S923 S924 24 = 4! x 4/4 = (5-5/5)!, etc. (see also below, following S936) S925, S926 S927 (corrected below, following S931) +76(28)513 X932 A wily chess puzzle: Sneaky trick X933 A clock puzzle: Hands at right angles X934 Another solitaire puzzle: From all-but-1 to only-1 in 16 moves X935 A chicken puzzle: * X936 Heard on the racecourse: S928, S929, S930, S931, S927 +76(28)604-606 Little Things That Puzzle Z28.1 How is the rat moved?: Trick cards Z28.2 A house of cards burgled: Card trick Z28.3 A coin trick: How to identify a coin blindfolded Z28.4 Very mental arithmetic: Forcing a sum Z28.5 A billiards puzzle: * Z28.6 How she knew: A preposterous conundrum Z28.7 How to hold an eel: Z28.8 A match trick: S932, S933, S934, S935, S936 S924 24 = (1+sqrt(1/.\dot1))! = (7-sqrt(7/.\dot7))! +77(29)62-63 X937 Domino squares: Three loops [not memorable] X938 The reapers' puzzle: * X939 Alphabetical order: The longest word of increasing letters X940 The Bath chair: * SZ28.1, SZ28.2, SZ28.3, SZ28.4, SZ28.5, SZ28.6, SZ28.7, SZ28.8 +77(9)208 X941 A necklace problem: How many with 8 beads and two colors? X942 Anagrammatic verse: Anagrams of a familiar nursery rhyme X943 Equal addition: Trick of wording X944 An episcopal visitation: Bishop's tour on 10x10 [sequel to P16 = AM325] S937, S938 S939 BEFILMS is his best [Eckler misses this one but has AEGILOPS] S940 77(29)312 X945 Cross-number puzzle: Has a more traditional format than X768 X946 Missing words: All words spelled the same X947 Halfpennies and tray: How many unit circles fit in circle of diameter 9? X948 Juggling with digits: a+b = c, d-e = f, gxh = ij, {a,...,j}={0,...,9} S941 "General solution ... difficult, if not impossible" [but MacMahon had in fact solved it long before] S942, S943 S944 He conjectures that 23 moves is shortest +77(29)416 X949 Easy draughts: (by Brooks) X950 The flagon puzzle: * X951 Finding a square: Which three of six given numbers sum to a square? X952 Queer addition: X953 Anagrams: S945, S946 S947 (see also below, following S962) S948 +77(29)482 X954 Three Greek crosses from one: A question posed in AM, page 168 X955 Easy arithmetic: ab...z x 4 = b...za x 5 X956 Card frames: a+b+c=c+d+e+f=f+g+h=h+i+j+a=22, {a,...,j}={1,...,10} X957 Pocket money: * S949, S950, S951 S952 (see also below, following S971) S953 +77(29)602 X958 A chess puzzle: (by Loyd) X959 A charade: X960 News boys: * X961 Correcting a blunder: Triangle with integer sides, height, and bisector X962 The longest palindrome: Longer than REVIVER? S954, S955, S956, S957 +78(29)91 X963 Stars and crosses: Cut 6x6 into four cong parts, each containing a star and a cross [cf X871] X964 Digital squares: abc^2 = defghi, {a,...,i}={1,...,9} X965 A rebus: X966 Antigrams: LEPER - REPEL; what's the longest? X967 A juvenile puzzle: Hopscotch board with one continuous stroke (Eulerian) S958 (see also below, following S971) S959, S960, S961 S962 RELEVELER (see also below, following S976) S947 +78(29)208 X968 The zigzag puzzle: [Reprise of X30] X969 City luncheons: * X970 Measuring the river: * X971 Easy draughts: S963, S964, S965 S966 (see also below, following S976) S967 +78(29)312 X972 Shifting cards: [Reprise of X27] X973 Buying ribbon: * X974 Arithmetical progressions: abc,def,ghi; acb,dfe,gih, {a,...,i}={1,...,9} X975 Geographical excisions: Word play, TRAVESTY - VEST = TRAY X976 A new boomerang puzzle: Find abc from (abc mod 11, bca mod 11, cba mod 11) S968, S969, S970, S971, S952, S958 +78(29)391 X977 A chess puzzle: (by Horwitz) X978 Broken cities: Eleven city names, fragmented X979 Square and cube: abcd = x^2, efghij = x^3, {a,...,j}={0,...,9} X980 Domino multiplication: Put 28 of them into seven dominetics S972, S973 S974 (see also below, following S985) S975, S976, S962, S966 +78(29)520 X981 A draughts ending: 3 kings versus 2 X982 Trading in oranges: * X983 Consonants and vowels: Longest word with one vowel X984 A complete skeleton: Skeletons for two related divisions X985 Lawn tennis: 8 couples on 4 courts in 7 days, never with spouse S977, S978, S980, S979 +78(29)661-663 Christmas Puzzle Chatter Z29.1 A strange coincidence: Identify a lady who is almost like George Eliot Z29.2 Horatio's clock puzzle: [Reprise of Z14.6] Z29.3 Mind your P's and Q's: Identify 5-letter words [PQ].... from definitions Z29.4 A letter square: Spell animal names as king paths Z29.5 The four ships: Make them equidistant [similar to Z16.4, with twist] Z29.6 A little arithmetical puzzle: Multiplication reverses the digits S981, S982 S983 STRENGTHS S984, S985 S974 "...large number of...easy solutions...now hardly worth correction." +79(30)102-103 X986 Counting the matches: * X987 Brick bond: Draw as much as possible in one continuous stroke X988 Consecutive numbers: Identify them from the pattern of their prime factors X989 The siege of Troy: A cute mate in 4 SZ29.1, SZ29.2, SZ29.3, SZ29.4, SZ29.5 SZ29.6 (see also below, following S993) +79(30)198 X990 Square and triangle: Fold a square to make an equilateral triangle X991 Holiday problem: * X992 Vowels and consonants: Longest alternating word like GENERAL X993 Pocket money: * S986, S988 S987 (see also below, following S1001) S989 +79(30)312 X994 The numbered frame: (a+...+f=(f+..+k)/2=(k+...+p)/3+(p+...+t+a)/4, {a,...,p}={1,...,20}, with fewest exchanges X995 Ring of animals: ELK - KANGAROO - OTTER - RAT etc X996 Square root skeleton: X997 Shifting the pieces: Without pawns, rotate init pos 90 deg in fewest moves S990, S991, S992, S993, SZ29.6 +79(30)404 X998 Easy draughts: X999 Digital divisors: Min and max abcdefghi, {1,...,9}, divisible by 1,2,...,9 X1000 Choosing a site: What point inside equilateral triang is closest to sides X1001 The engine-driver's name: Logic puzzle S994, S995, S996, S997 +79(30)520 X1002 A teasing chess puzzle: [Reprise of Shinkman's X184] X1003 Permuted digits: * X1004 A charade: X1005 Painting a tetrahedron: With two colors in all ways [He explains a nice way to make paper tetrahedron from an envelope] S998, S999 S1000 [Was his joke for number 1000] S1001 S987 He says he can increase the length to 304, possibly more +79(30)640 X1006 The encircled triangles: Draw with few continuous strokes X1007 A railway carriage number: abcda divisible by d and by the prime bcd [and also by 64, but that fact isn't necessary since 10001 = 73x137] X1008 Ring of birds: A sequel to X995 X1009 Dividing by nine: Trick S1002, S1003, S1004, S1005 +80(30)112 [Beginning with this issue, published in July 1930, the Perplexities page no longer carried a byline; Henry E. Dudeney, who was specifically credited with all columns from May 1910 until June 1930, had died on 24 April 1930. The column continued to appear monthly until The Strand Magazine ceased publication in the 1950s; but, perhaps appropriately, Dudeney's own final Perplexity had the prime number 1009 = MIX.] S1006, S1007, S1008, S1009 ---------------------------------------- In the cross-references, P stands for problems in The Weekly Dispatch, T for problems in Tit-Bits, CP for Canterbury Puzzles, AM for Amusements in Mathematics, MP for Modern Puzzles, PCP for Puzzles and Curious Problems, LC for Loyd's Cyclopedia, and WP for Dudeney's 300 Best Word Puzzles [in Martin Gardner's edition of 1968]. ---------------------------------------- X1 = P535, AM224 X2 = WP241 X3 = P334, AM12 X4 = AM383 is equivalent to AM277 X5 is a simpler version of AM309 X7 = P287, AM274 X9 = AM80 X10 = P347 is similar to (but less elegant than) AM215 X11 = PCP257 X12 = WP144 X13 = AM279 is simplified version of P444 X15 = P403, AM31 X16 = P508, AM139 X17 = P351, AM249 X18 = P288, AM146 X19 = P390, AM237, PCP252 X20 is a simplification of AM253 X21 = P349, AM93 X22 = AM56, PCP39 X23 = AM267 X28 = P229, P496, AM209 X29 = AM171 X33 = AM389 X34 = AM362 X36 = AM329 X37 = P172, AM275 X39 = AM265 X40 = P262, AM341 X41 is almost identical to Z09.19 X42 = AM360 X43 = P193, AM223 X45 = AM150 X46 = AM23 X47 = AM252 X48 = AM95 X49 = AM317 is a simplification of P324 X50 = AM21 X51 = AM326 X52 = PCP193 X53 = AM366 X54 = AM204 X55 = AM266 X56 = P434, AM217 X57 = P475 X58 = PCP196 X60 = AM384 X62 = AM323 is similar to P161 X64 = AM43 X65 = AM202 X66 = P478 X68 = PCP232 X69 is equivalent to AM220 X70 = AM1 X72 is similar to MP10 X73 = AM248 X75 = AM13 X78 = AM380 X79 = AM178 X82 = AM225 X83 = AM115 X84 = AM356 X85 = AM306 X86 = WP170 X87 = AM268 X88 = AM234 X89 = AM101 X90 = P531, AM63 X91 = AM247 X92 = AM219 = WP294 is a simplification of P12 X93 = AM421 X94 = PCP250 X95 = P458, AM25 X96 = AM167 X97 = PCP260 X98 = AM203, MP211 X99 = AM126 X100 = AM334 X101 = AM147 X102 = AM240 X103 = AM260 X104 = AM24 X105 = AM415 X106 = AM339 X107 = AM235 X108 = P486, AM180 X109 = AM153 X110 = AM396 X111 = PC1(1896.12.13), AM211 X112 = P139, PCP338 X113 = P1 X114 = P19 is (in part) mentioned in WP page 51 X115 = P11, WP192 X116 = P219, AM77 X117 = AM111 X118 = AM205 X119 = P191, AM26 X120 = P31, WP74 X121 = P34 X122 = P3, WP138 X123 = P175, PCP303 X124 = AM175 X125 = WP29 X126 = WP75 X127 = P200, PCP259 X129 = AM127 X131 = AM165 X132 = WP297 X133 = P86, WP86 X134 = P384, AM226 X135 = P454, PCP282 X136 = AM102 X137 = PCP359 X138 = P415, AM183 X139 = WP123 X140 = AM332, MP151 X141 = AM365 X142 = AM347 X143 = AM114 X144 = P106, WP139 X145 = AM125 X146 = AM251, MP156 X147 = AM239 is the first part of MP157 X148 = WP31 X149 = AM140 X150 = AM208 X151 = AM54 X152 = AM406 X153 = P122, AM6 X154 = P82, WP128 X155 = AM214 X156 = AM391 X157 = AM241 X158 = AM11 X159 = MP21 X160 = AM372 X161 = AM103 X163 = AM151 X164 = AM333 X165 = AM42 X167 = AM216 X168 is a simplification of P381, AM158 X169 = AM285 X170 = AM23 X171 = P8, AM230 X172 = P39, AM45 X173 = P9,WP174 X174 = P89, WP224 X176 = PCP353 X177 = P51, WP187 X178 = AM278 X179 = AM179 X180 = PCP319 X181 = AM15, MP4 X182 = P29, WP136 X183 = AM429 X186 = WP30 X187 = AM327 X188 = P446, AM422 X189 = AM89 X190 = WP147 X191 = P527, AM138 X192 = AM414 X193 = AM416, MP219 X194 = AM386 X195 = MP195 X196 = P101, PCP166 X197 = AM228 X198 = P121, WP90 X200 = PCP277 X201 = MP162 X202 = MP149 X203 = WP176 X204 = WP267 X205 = AM405 X206 = MP99 X207 = MP103 X208 = AM69 X209 = WP175 X210 = P423, AM244 is similar to PCP209 X211 = P466 X212 = PCP318 X213 = AM104 X214 = WP196 X215 = PCP270 X216 = AM74 X218 = MP1 X219 = WP221 X220 = P318, AM343 X222 = PCP271 X223 = P302, MP38 X224 = WP98 X225 = PCP360 X226 = PCP347 X227 = WP296 X228 = WP99 X230 = LC286, PCP142 X232 = P247, AM118 X234 = PCP326 X235 = WP271 X237 = PCP153 X238 = MP118 X239 = MP87 X240 = PCP67 X242 = PCP154 X243 = MP147 X244 = PCP66 X246 = PC4(1903.12.20), MP114 X247 = P457, MP92 X248 = MP154 X249 = WP18 X251 = PCP251(!) X252 = PCP306 X254 = WP133 X256 = MP206 X257 = PCP220 X258 = WP212 X259 = WP204 X261 = MP177 X264 = PCP344 X265 is similar to P283, PCP283 X266 = P276, AM94 X267 = MP146 X269 = AM272, PCP287 X272 = MP69 X273 = WP84 X274 = AM385 X276 = MP116 X277 = WP214 X279 = MP178 X280 = WP188 X281 = WP63 X283 = T49, AM218 X284 = AM322 X285 = MP169 X286 = WP62 X287 = WP94 X288 = AM66 X289 = WP10 X292 = WP295 X293 = MP165 X294 = WP230 X295 = AM76 X296 = AM58 X297 = WP151 X298 = MP152 X299 = WP239 X300 = MP215 X301 = WP157 X303 = WP299 X304 = AM98 X305 = MP207 X307 = MP203 X309 = MP186 X311 = P93 X314 = WP141 X316 = P33 X317 = WP241 X319 = P484 X320 = P233 X321 = P35, WP125 X323 = AM73 X325 = WP27 X326 = PCP285 X327 = WP203 X328 = MP179 X330 = MP163 X331 = PCP218 X333 = P460, AM157 X335 = PCP58 X336 = WP287, an extension of P245 X337 = MP220 X338 = MP91 X339 = MP124 X340 = MP43 X341 = WP278 X342 = P404, AM246 X343 = MP222 X346 = PCP76 X347 = PCP169 X350 = P98, WP81 X351 = MP199 X352 = P522 X353 = PCP308 X354 = PCP34 X357 = P215 X358 = MP137 X359 = MP84 X360 = WP143 X361 = P325, AM342 X363 = P291, AM148 X364 = MP79 X365 = WP229 X366 = WP244 X369 = WP242 X371 = WP263 X372 = MP164 X373 = WP166 X374 = WP78 X375 = PCP281 X376 = MP22 X377 = WP131 X379 = WP14 X381 = MP25 X383 = PCP20 X384 = WP73 X386 = MP35 X387 = WP257 X388 = Z96.1 X389 = AM397, MP205 X390 = WP124 X391 = WP171 X393 = AM86, PCP108 X394 = P110, WP127 X396 = PCP192 X397 = PCP228 X398 = PCP47 X399 = WP165 X400 = MP141 X401 = MP16 X402 = WP253 X403 = P102, WP82 X405 = MP208 X406 = MP198 X407 = MP36 X408 = WP213 X409 = MP135 X410 = WP142 X411 = WP76 X413 = PCP331 X414 = P170 X416 = P42, WP71 X417 = WP12 X418 is somewhat similar to P293, CP42, and uses the same illustration X419 = WP234 X420 = P299 X421 = WP288 X422 = MP142 X423 = WP185 X424 = P25, PCP170 X426 = P160, PCP145 X427 = P466 X428 = PCP112 X429 = PCP191 X430 = WP page 2 X432 = WP145 X433 = PCP165 X434 = WP285 X436 = P43, WP189 X437 = MP136 X438 = MP60 X441 = P38, WP137 X442 = PCP324 X444 = MP128 X445 = WP89 X446 = WP227 X449 = WP page 5 X452 = MP34 X453 = MP175 X454 = MP54 X455 = PCP280 X456 = PCP164 X458 = WP180 X459 = WP233 X460 = MP138 X461 = WP205 X462 = PCP313 X464 = MP45 X465 = WP182 X466 = MP53 X467 = PCP213 X469 = MP139 X471 = MP119 X472 = WP page 1 X474 = MP58 X475 = WP292 X476 = MP56 X477 = MP125 X478 = WP195 X481 = PCP16 X482 = MP217 X483 = WP100 X484 = PCP23 X485 = PCP179 X486 = MP6 X487 = P541, PCP188 X488 = WP156 = WP284 X489 = WP201 X490 = MP214 X491 = PCP80 X492 = PCP305 X494 = WP200 X497 = PCP356 X498 = WP209 X500 = MP20 X501 = P391 X502 = WP261 X503 = PCP26 X505 = PCP355 X506 = WP97 X508 = PCP173 X509 = WP259 X510 = WP167 X511 = WP279 X512 = P385, PCP187 X514 = WP276 X515 = PCP255 X516 = MP80 X517 = WP190 X518 = MP180 X519 = WP262 X520 = T38, MP204 X522 = MP55 X523 = MP111 X524 = WP1 X525 = MP31 X527 = WP16 X528 = PCP190 X529 = MP86 X530 = MP181 X532 = WP211 X533 = P1 X534 = WP4 X536 = MP65 X537 = PCP213 X539 = WP282 X540 = MP145 X542 = MP132 X543 = WP page 3 X544 = PCP87 X545 = AM359, MP150 X546 = WP2 X547 = WP286 X549 = PCP73 X550 = MP117 X551 = WP277 X552 = P191, PCP37 X553 = WP5 X554 = MP121 X558 = PCP266 (and it is similar to P471) X559 = MP201 X560 = WP255 [see Hoffmann's 5.1] X561 = MP82 X562 = WP150 X563 = MP209 X564 = WP123 X565 = MP8 X566 = MP98 X567 = MP109 X568 = MP72 X569 = MP130 X570 = WP235 X571 = PCP27 X572 = WP page 4 X573 = MP63 X576 = MP39 X577 = MP24 X578 = WP77 X579 = MP122 X580 = MP50 X581 = MP29 X582 = MP221 X583 = WP254 X585 = MP26 X586 = WP283 X587 = MP188 X588 = MP148 X589 = MP83 X591 = WP3 X592 = MP51 X594 = PCP141 X595 = MP52 X596 = P119, WP72 X598 = WP186 X600 = WP216 X601 = PCP135 X602 = MP155 X604 = WP23 X605 = PCP237 X606 = PCP107 X607 is similar to PCP97 X608 = PCP222 X609 = WP206 X610 = WP87 X612 = MP19 X614 = WP15 X615 = PCP207 X616 = P63, WP129 X618 = PCP230 X619 = WP93 X620 = T5, WP293 X621 = WP207 X626 is equivalent to PCP211 X627 = MP70 X628 = WP22 X630 = WP266 X631 = PCP210 X632 = AM368, PCP294 X633 = WP152 X634 = MP94 X635 = PCP337 X636 = PCP4 X637 = PCP289 X639 = WP194 X640 = MP104 X641 = MP71 X642 = P135, WP135 X643 = MP46 X644 = WP240 X645 = PCP312 X646 = MP61 X647 = WP208 X648 = MP42 X649 = P123, MP126 X652 = MP131 X653 is similar to PCP97 X654 = MP183 X655 = WP215 X656 = PCP336 X657 = WP168 X658 = PCP209 X659 = WP13 X660 = MP96 X662 = PCP95 X664 = MP47 X665 = MP158 X666 = WP210 X667 = MP134 X668 = MP73 X669 = WP8 X670 = MP194 X671 = MP191 X672 = WP9 X674 = WP95 X676 = PCP2 X677 = PCP208 X678 = WP91 X682 = MP97 X683 = WP96 X684 = MP67 X686 = WP148 and WP page 48 X687 = P91, WP184 X688 = MP57 X689 = PCP206 X690 = MP3 X692 = MP68 X693 = P95, WP134 X694 = MP167 X695 = WP19 X696 = PCP40 X699 = MP62 X700 = MP7 X701 = WP70 X704 = PCP140 X705 = WP197 X706 = WP24 and WP25 X707 = MP184 X709 = PCP307 X710 = MP105 X711 = WP92 X713 = WP236 X714 = MP90 X715 = T38, MP204 X716 = PCP106 X718 = WP79 X719 = WP268 X722 = MP40 X723 = WP280 X724 = PCP163 X725 = MP153 X726 = MP185 X728 is similar to P55 X730 = WP237 X731 = MP173 X732 = P78, WP83 X733 = MP174 X735 = PCP186 X736 = MP197 is similar to P192 X737 = WP281 X738 = WP248 X739 = MP64 X740 = WP177 X741 = MP11 X742 = WP80 X743 = WP250 X744 = MP49 X745 = WP228 X746 = PCP284 X747 = WP85 X748 = WP252 X749 = PCP227 X750 = WP17 X751 = WP198 X753 = WP251 X754 = PCP72 X756 = PCP339 X757 = WP249 X758 = MP23 X759 = PCP204 X760 = MP59 X764 = MP33 X765 = WP183 X766 = PCP149 X767 = WP284 X773 = MP190 X774 = MP66 X776 = P268, AM423 X777 = MP196 X778 = MP95 X779 = PCP171 X780 = PCP111 X783 = PCP42 X793 = PCP180 X794 = PCP309 X798 = MP74 X802 = PCP15 X804 = PCP314 X805 = LC244, PCP137 X806 = PCP86 X808 = PCP14 X809 is similar to PCP215 X810 = PCP65 X812 = PCP124 X819 = PCP351 X820 = PCP229 X822 = LC288, PCP185 X824 = PCP83 X825 = PCP30 X826 = PCP110 X828 = PCP318 X830 = PCP246 X834 = PCP77 X836 is related to P201 X839 is related to P253 X840 = P286, PCP147 X841 = PCP184 X844 = PCP183 X845 = PCP162 X846 = PCP55 X852 = PCP167 X853 = PCP56 X857 = PCP125 X858 = PCP182 X859 = PCP74 X861 = PCP161 X862 = PCP51 X865 = PCP119 X867 = PCP224 X870 = PCP120 X872 = PCP340 X874 = PCP105 X876 = PCP292 X877 = PCP99 X878 = PCP160 X885 = PCP310 X887 = PCP54 X890 = PCP262 X892 = PCP203 X895 = P145 X899 = PCP159 X903 = PCP202 X906 = PCP89 X908 = PCP346 X909 = PCP25 X910 = PCP276 X911 = PCP296 X913 = PCP90 X915 = PCP104 X918 = PCP91 X919 = PCP261 X921 = PCP53 X924 = PCP103 X925 = PCP290 X927 = PCP345 X929 = PCP129 X931 = MP197 X933 = PCP62 X938 = PCP35 X940 = PCP64 X941 = PCP275 X945 = PCP175 X947 = PCP274 X948 = PCP102 X950 = PCP36 X951 = PCP101 X954 = PCP181 X955 = PCP116 X956 is similar to AM381 X959 = WP107 X960 = PCP158 X961 = PCP242 X963 = PCP178 is almost the same as AM289 X964 = PCP100 X967 = PCP333 X969 = PCP273 X970 = PCP200 X973 = PCP50 X980 = PCP311 X984 = PCP113 X986 = PCP157 X990 = PCP201 X1000 = PCP328 X1001 = PCP49 X1005 is a simplification (to two colors) of P448, AM281 X1006 = P368, PCP330 ---------------------------------------- Z08.1 = AM350 Z08.2 = AM316 is a simplification of P309 Z08.3 = AM313 Z08.4 = AM357 Z08.7 = P244, AM319 Z08.8 = AM348 Z08.9 = AM355 Z08.10 = AM353 Z08.X = P222, AM346 Z08.13 = PCP304 Z08.15 = MP193 is similar to P316, AM406 Z08.16 = T38, MP204 Z08.17 = P312, AM227 Z08.18 = P521, AM304 Z08.19 = P459 Z08.20 = AM193, PCP241 Z08.21 = AM192 [it had previously appeared in The Captain, Jan 1900] Z08.23 = P432, AM199 Z08.24 = AM110 Z08.27 = P396, AM417 Z08.31 = T54, AM315 Z08.32 = AM310 Z08.34 is similar to P188, PCP189 Z08.36 = P108, AM236 Z08.39 = P209, AM424 Z08.41 = P179 and P388; part of it appears in AMp56 Z08.43 = AM421, is similar to T25 Z08.44 = P501, CP75 Z08.45 = P440 Z08.46 = AM232 Z09.1 = AM419 Z09.3,Z09.4,Z09.5 = AM28 Z09.7 = AM284 = PCP247 is related to P243, CP4 Z09.8 = PCP247 Z09.9 = PCP293 Z09.10 = P4, CP67 Z09.11 = CP27, similar to P72, AM358 Z09.12,Z09.13,Z09.14 = P328, AM233 Z09.15 = P246, AM210 Z09.17 = AM231 Z09.18 = P259, AM221 Z09.19 is a greatly simplified version of P192 Z09.21 is similar to P412, see AM page 151 Z09.22 = P142, AM27 Z09.23 = P195, AM29 Z09.24 = AM30 (first part) Z12.1 = AM52 Z12.2 = AM123 Z12.4 = AM363 Z12.5 = PCP6 Z12.7 = AM229 Z12.8 = PCP301 Z12.9 = AM392 Z13.1 = WP291 Z13.2 = AM75 Z13.2+ = WP269 Z13.3 = AM198 Z13.5 = AM168 Z13.7 = AM99 Z13.8 = AM72 Z13.9 = AM294 Z13.10 = PC5(1903.12.20), AM109 Z14.1 = MP85 Z14.2 = P339, AM143 Z14.3 = PCP24 Z14.4 = MP151 Z14.5 = P306 Z15.1 = P268, AM423 Z15.8 = P271 Z15.9 = Weekly Dispatch puzzle M1 of 1903.04.19 Z16.4 is simplification of T34 Z16.6 = MP127 Z16.7 = PCP217 Z16.9 = WP298 Z16.11 is similar to PCP359 Z16.12 = WP153 Z16.13 = WP154 Z16.15 = P534, WP53 Z16.16 = WP231 Z16.17 = WP290 Z16.18 = WP273 Z17.1 = WP116 Z17.5 = WP20 = WP114 Z17.6 = MP144 Z17.9 = MP78 Z17.10 = MP192 Z17.12 = WP289 Z17.13 = PCP300 Z17.14 is a simplification of AM299 Z18.1 = WP264 Z18.2 = MP44 Z18.3 = WP191 Z18.4+ = WP169 Z18.5 = PCP121 Z18.6 = PCP254 Z18.9 = T36, MP89 Z18.10 = WP27 Z18.11 = MP187 Z19.1 = WP69 Z19.3 = PCP43 Z19.4 = PCP199 Z19.5 is a simplification of T54 Z19.7 = PCP219 Z20.4 = MP32 Z20.6 = MP189 Z20.7 = WP155 Z20.8 = WP226 Z20.10 = MP218 Z21.1 = PCP12 Z21.2 = WP217 and WP26 Z21.4 = MP48 Z21.5 = MP106 Z21.6 = AM119 Z21.8 = P503, WP55 Z21.10 = MP129 Z22.5 = WP88 Z22.6 = MP143 Z23.1 = PCP9 Z23.2 = P184, MP30 Z23.3 = PCP21 Z23.5 = WP6 Z23.6 = PCP195 Z23.9 = MP102 Z24.2 = MP41 Z24.3 = WP172 Z24.4 = MP170 Z24.5 = MP133 Z24.7 = P23, WP199 Z24.10 = P47, WP130 Z24.11 = MP168 Z25.1 = MP101 Z25.2 = PCP364 Z25.5 = PCP240 Z25.7 = WP238 Z25.8 = PCP71 Z25.9 = WP24 Z25.10 = MP107 Z25.11 = WP page 26 Z25.12 = MP212 Z26.1 = PCP131 Z26.2 = PCP350 and is similar to P438 Z26.3 = PCP93 Z26.4 = PCP348 Z26.6 = PCP127 Z26.11 = PCP223 Z26.12 = AM145 [it had previously appeared in Cassell's Magazine, Dec 1909] Z27.1 is partly P57 Z27.5+ = WP274 Z27.8 = PCP359 Z27.13 is a slight extension of P195 = AM29 Z28.8 = PCP334 Z29.5 = T34