Dudeney and Loyd's columns in Tit-Bits [with occasional notes of my own]
Dudeney made occasional contributions early in 1896; Loyd joined him
on September 26, contributing regularly until 1897.08.21 and sporadically
thereafter. At about the same time Loyd was writing for the Brooklyn Daily
Eagle, using similar material cited as "BDE" below. Dudeney allowed the
column to taper off in 1898, most likely because he was becoming overwhelmed
with work for The Weekly Dispatch and other occasional publications.
(c) 2001 Donald E Knuth [but freely downloadable for personal use in research]
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1896.06.09 The fifteen-letter puzzle (Dudeney): Steiner triple system on
the letters ABCDEFGHIJKLMNO, maximizing the number of common 3-letter words
1896.06.20 Solution [repeated later in P372 and AM271] has 21 such words
1896.09.26 Loyd's introductory essay: The world of puzzledom
1896.10.03
T1 The two squares puzzle: dissect axa + bxb into cxc
[All puzzles T1, T2, ..., T48 are by Loyd; solutions called S1, S2, ...]
1896.10.10
S1 with two cuts (three pieces) proves Pythagoras most elegantly
T2 The Greek cross: dissect 1+3+1 into a square [BDE 1896.04.05]
1896.10.17
S2 with two cuts (four pieces)
T3 The three squares: dissect 1x3 into a square [BDE 1896.11.15]
Example of the step principle
1896.10.24
Comments on the 15-puzzle
1896.10.31
Loyd claims 47 ways to dissect 2x2+1x1 into cxc; but Dudeney advises readers
not to try it
T4 The Swiss flag: dissect flag - cross + pole into square [BDE 1896.10.26]
1896.11.07
T5 The switch puzzle: 12-letter word to reproduce itself vertically
after 12 moves [BDE 1896.07.26]
1896.11.14
T6 The boarding-house pie: maximum pieces after 7 straight cuts of a circle
[A problem solved by Steiner in 1826, but Dudeney wants also the "most
equitable" such division]
S3 in three pieces
1896.11.21
T7 A problem in cheese: maximum 3D pieces after 7 straight cuts
[BDE 1896.05.10 had 6 cuts]
S4 combines step principle with Pythagoras
1896.11.28
T8 Motto rebus: verbal/visual puzzle [BDE 1897.01.17]
S5 "INTERPRETING", not "COOCOOCOOCOO" [Note: My program LOYDWORDS finds that
the word "POSTPONEMENT" would make a similar puzzle]
1896.12.05
S6 a solution with 7-fold symmetry; no proof of best size distribution
T9 The eagle problem: how long to fly around globe from London, 3000 miles west
every day and 2000 east every night [BDE 1896.05.24]
1896.12.12
S7 shows the cuts; hilarious comments by readers
T10 Counting the pieces: how many pieces are formed by the procedure in S7?
1896.12.19
Loyd calls measuring puzzles "jug-gling tricks"
T11 Two thieves of Damascus: get (2,2) from hogshead in pails of sizes (5,3)
S8 On ST is the better Poll I see
1897.01.02
S9 Loyd gets correct answer by making two mistakes; Dudeney says it right
T12 The temperance puzzle: count routes of REDRUM&MURDER [BDE 1897.01.10]
1897.01.09
T13 The oriental problem: given 63gal of water plus 31.5gal of honey plus
three 10gal bottles plus 4gal and 2gal measures, measure out 3gal of
water for each of 13 camels and fill the bottles with (3water,3honey,
3water+3honey) without discarding any water or honey, in fewest operations
[BDE 1896.04.12 had the same problem but without camels]
S10 64 pieces; no explanation given [see Concrete Math, problem 1.14]
1897.01.16
S11 requires wasting lots of beer
T14 A crow puzzle: 8 queens with no three in a line [BDE 1896.12.20]
1897.01.23
S12 372x372
T15 The gaoler's problem: rook's tour d5 to d5 with fewest turns
[BDE 1896.08.16]
1897.01.30
T16 The captive maiden: rook tour h1 to a8 with fewest turns [BDE 1896.11.29
asked for h2 to a8; Dudeney in TWD P20 had previously asked for h1 to a8
but without requiring fewest turns]
S13 in 521 moves [computer verification would be desirable]
1897.02.06
T17 Ye castle donjon: dissect 5x25 into two pieces allowing a rook tour
[BDE 1896.06.07]
S14 unique
S13 improved to 513 moves, but the solution not stated [Loyd's Cyclopedia p188
has 506-move solution, which Dudeney said he found; cf Strand (April 1926)]
1897.02.13
T18 An ancient puzzle: cut L-tetromino into 4 congruent pieces
T19 The mitre puzzle: same for square minus triangle [BDE 1896.11.01]
S15 nearly everybody thought 17 moves needed, but 16 win
1897.02.20
T20 hearts and darts: cover 8x8 by fewest connected lines, starting on the
diagonal [BDE 1896.08.23]
S16 after backtracking for parity, 20 more moves suffice ("two or three" ways)
1897.02.27
T21 The eccentric gardener: 10 pear trees in 5 lines of 4, pack into 8x8-2x2,
with as many as possible adjacent to the 2x2 at the bottom
[Dudeney gives similar puzzle P162 in TWD 1897.03.07: 2x2 now in center]
S17 sneaky way to remove a cell by cut of slope 25/1
1897.03.06
Discussion of the "odds and evens principle" (parity)
T22 A little linoleum puzzle: dissect a checkered 8x8 and 6x6 into 10x10
[BDE 1897.02.14]
S18, S19
1897.03.13
T23 The square and cross: dissect a square into 4 congruent pieces that make
a Greek cross [BDE 1896.10.04]
1897.03.20
S21
T24 More eccentric gardening: four disjoint solutions of 10 points in five
lines of 4, in 8x8-2x2 [BDE 1897.02.07]
S20 unique solver (also of S13) was Frank Inglis of Glasgow, 14 queen moves
1897.03.27
T25 The chain puzzle: 13 chains to be joined [similar to BDE 1896.11.22]
T26 A study in naval warfare: sink 8x8 starting at h4 [BDE 1896.07.12]
S22
1897.04.03
S23 the square is cut by a swastika
T27 The swastika problem: cut square into 4 congruent pieces, make two crosses
1897.04.10
T28 A railway puzzle: trains pass [BDE 1897.03.14]
S24 seems to be unique
1897.04.17
T29 the old beacon tower: length of a helix [BDE 1897.03.21]
S25
1897.04.24
S27
T30 The Easter problem: dissect square into five pieces, make two Greek
crosses of unequal size
S26 another 14-line solution, this time using slope 1/2
1897.05.01
T31 The turn-table puzzle: reverse an engine and nine cars [BDE 1897.04.11]
S28
1897.05.08
T32 The patchwork quilt puzzle: rearrange 12x12 square and isosceles right
triangle of area 25 to make a square [BDE 1897.01.24]
T29a The Nelson Column puzzle (Dudeney): another helix
1897.05.15
T33 The kangaroo puzzle: 12-letter word jumps down [BDE 1896.12.13]
S29 and S29a, quite different!
S30
1897.05.22
T34 War-ships at anchor: position four ships equidistant from each other
S31
1897.05.29
T35 Solitaire muggins: find the maximum score of a domino game
[used later in TWD 1901.01.20 as P366]
S32
1897.06.05
T36 Juggling with figures (by W. T. W.) [probably W. T. Whyte, who also
submitted a solution hoping for the prize --- see 1897.07.03]:
solve a x b = c using {0,1,...,9}, minimizing c
T37 A queer legacy: divide 17 horses in proportion 1/2 to 1/3 to 1/9
[BDE 1897.04.04]
S33 "...belongs to a class that is not greatly admired either by Mr Loyd
or myself"; WOOLOOMOOLOO in 20; SUCCESSFULLY, HEEDLESSNESS, ... take 21
1897.06.12
T38 The twenty-five-up puzzle: version of 1-pile nim, must go to adjacent sides
of a die (thus after x must choose from {1,2,3,4,5,6} \ {x,7-x})
S34 finds a tetrahedron on the earth's surface
1897.06.19
T39 Septimal currency: what is 1/10 in radix 7?
S35 unique (?) way to achieve 195 [computer verification desirable]
1897.06.26
T40 The Persian rug puzzle: dissect 1x2 rectangle minus corner to square
1897.07.03
T41 The Swiss ferry puzzle: six people cross a river with restrictions
S36 3907x4=15628; Dudeney says the max is 9403x7=65821; working mod 9 helps
S37, S38
1897.07.10
T42 The blacksmith puzzle: another twist on joining ten chains
S39 (.046204620462...)_7
1897.07.17
T43 The daisy game: Kayles with 13 petals [BDE 1896.10.18]
S40
1897.07.24
T44 A fractional magic square: 5x5 from {8x1,8x4,2x5,2x6,4x7,1x9} and dec pts
S41
1897.07.31
T45 The whirlpool puzzle: shortest path, a precursor of Loyd's Klondike puzzle
[NY Journal 1898.04.04, also used in promotion for Pond's extract 1899]
S42
1897.08.07
T46 Practical railroading: Chinese postman path on a certain 8-edge tree
S43
1897.08.14
T47 The two warders: simultaneous rook tours a1<->h7 in 21 turns, never meeting
S44 uses 26 decimal points, with .999999999999999 = 1 in the center
1897.08.21
T48 A jubilee problem: geometry based on garlands in the parade
S45 in 5 jumps and distance 11
1897.09.04
T49 The Victoria cross (Dudeney): 8-puzzle to make an odd cyclic permutation
of the word VICTORIA, empty in the center
S46 would have been easy, but Loyd concealed clues with an optical illusion!
S47 several solutions
1897.09.11
T50 A problem in mosaics (Dudeney): queens in 8 colors on 62 cells (8x8-a1-h1)
S48
1897.09.18
T51 The grindstone puzzle (Loyd): when has it been half worn away
[BDE 1896.08.09]
1897.09.25
T52 A fence problem (Dudeney): enclose as many acres of square field as there
are rails in the fence
S49 the 22 steps 'A VICTOR A VICTOR A VICTOR I' are interesting, but there's
a minimum solution in 18 moves
1897.10.02
T53 Quarrelsome neighbors (Loyd): connect 8 houses to 8 gates [BDE 1897.02.28]
S50 claims a unique solution except for colors swapped at two vertices
1897.10.09
T54 The hat-peg puzzle (Dudeney): find four adjacent 5-queen coverings of 8x8,
starting with all in a column, ending with no two attacking
[Note: Henceforth all problems T55, T56, ... are by Dudeney]
S51
1897.10.16
T55 The four princes puzzle: four distinct right triangles with same area
[Loyd may have published this in BDE 1897.04.18, but perhaps his problem
was less restricted; see also P445 in TWD 1902.05.11 and CP107]
S52 501760 acres and 501760 rails (at 14 rails per pole)
1897.10.23
T56 Two new cross puzzles: dissect 1x2 and isosceles rt triangle to Greek cross
S53 a truly amazing maze
1897.10.30
T57 The commercial traveler's puzzle: count routes corner to corner in 10x12
S54 claims there are 728 solutions of 5 queens covering 64 but not attacking
each other, if I understand D's wording
1897.11.06
T58 A wreath puzzle: name of flower having pattern abcdedfb [variant of
P165 published 1897.03.28 in The Weekly Dispatch]
S55 (47560,49938), (28536,83230), (17835,133168), (1681,1412880)
[much smaller solutions, claimed smallest, are in answer to CP107]
1897.11.13
T59 A multiplying magic square: 3x3 with 8 equal products, using fewest digits
[P181, in TWD 1897.07.18, didn't include the fewest-digit criterion;
P483, in TWD 1902.12.28, did]
S56
1897.11.20
T60 The hymn-board poser: how many digit-plates needed for all choices of
five hymns among {1,2,...,500}?
S57
1897.11.27
T61 An Indian frontier problem: fewest points, 10 lines of 3
[the idea developed further in P388, TWD 1901.06.23]
S58 BLUEBELL or MARITIMA
1897.12.04
T62 The five crescents of Byzantium: 5-queen cover avoiding largest square
[P163 in TWD 1897.03.14 asked to avoid the largest rectangle]
S59 18 1 12/4 6 9/3 36 2 has 12 digits; 5 .1 2/.4 1 2.5/.5 10 .2 has only 11
1897.12.11
T63 A lesson in linoleum cutting: T22 revisited, cutting least from the 8x8
S60 plates can be printed on both sides, and 6s can become 9s
1897.12.18
T64 The lockers puzzle: three solutions to abc+def=ghi from {0,1,...,9}; the
three ghi's must have distinct digits and must include the extreme values
S61
1898.01.01
T65 The Spanish dungeon: 15-puzzle, 1 2 3 4/.../13 14 15 0 -> magic square
T66 The sixteen puzzle: Halma-like interchanging 8 with 8 on 3+3+5+3+3
S62 elegantly avoids sqrt32 x sqrt32 in the middle
S63 needs to cut only 12 squares from the 8x8
1898.02.05
T67 One acre and a cow: what length rope makes circles intersect in one acre?
T68 Crossing the river Axe: three men with their booty must cross in small boat
S64 107+249=356(min), 134+586=720, 235+746=981 (max)
S65 37 moves [needs computer verification]
S66 correct solution in 46 moves published for the first time [again needs
verification; do we gain if can jump over own color and/or move back?]
1898.03.05
T69 The well puzzle: geometry
T70 The eight villas: count nonneg integer sols to a+b+c=c+d+e=e+f+g=g+h+a=9
S67, S68
1898.04.02
S69
S70 with general formula when 9 is replaced by n
---------------------------------------------
Connections with The Canterbury Puzzles:
CP89 is similar to T58
CP107 = P445
-------------------------------------------------
Connections with Amusements in Mathematics:
AM79 = T64
AM117 = T52
AM p33 is related to T56
AM176 = T63
AM213 is similar to T61
AM218 = T49
AM253 is similar to T57
AM276 = T70
AM302 is similar to T50
AM312 = T62
AM315 = T54
AM374 = T68
AM403 = T65
AM p124 is related to T59
AM421 is related to T25
AM426 = T60
-------------------------
Connections with Puzzles and Curious Problems:
PCP291 = T51