I found the following problem in the book M. Gardner, **My best math and logic puzzles**, Dover

White to play and **not** mate in 1.

I found the following problem in the book M. Gardner, **My best math and logic puzzles**, Dover

White to play and **not** mate in 1.

I found the following problem in the book C. Bandelow, **Inside Rubik’s cube and beyond**, Birkhauser, 1982

**White to play and mate in 182 moves. **

Here are the pieces and their locations:

Black pieces:

- pawns at b3, b6, c7, g4, g6, g7, h7
- knights at a8, f1, h3
- bishops at a7, g2
- rook at h2
- king at h1

White pieces:

- pawns at b2, b5, c6, g3
- knights at d1, e2
- rook at e1
- king at d8

solution below

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This is a Dec 5, 1999 email from Dror Efraty, with some minor edits:

hi David,

…

I send you my analyzis of the solution.

this is my analisis of the position:

in the given position few black pieces can move.

if Nh3 moves white mates in 1 move: Nf2#

if Bg2 moves, white mates in 2 – 1. R:f1 Kg2, 2. Ne3#

so black can only move with his king side pawns, and with Ba7.

note that after black captures g3 with his pawn (and later, when he moves

other pawns to g3) he can move Nf4 next move, and no mate is possible.

thus immidiately after black has a pawn on g3, white must move:

1. N:g3+ Kg1, 2. Ne2+ Kh1 to remove black’s pawn from g3.

this means, that if white kills black’s Ba7 and queen side pawns, black

must move with either Nh3 or Bg2, which result in mate in 2. but this is

not so easy for white to kill Ba7. the obvious way will be to move Kb7,

but then black move: B:c6+ and kg2 to release the position. then, black

has enough to win the game. also, if white’s king moves to almost every

other white square on the board, black can check him with either Bg2 or

Nh3, and release the position.there are 2 exceptions: c8 (current

position) and a4.

now, white can only kill black’s Ba7 on b8 and not on a7. but this can’t

happen if all white’s moves are king moves on black squares, because then

it takes white an even number of moves to return with his king to c8, and

during that time black moves Ba7-b8-a7-b8-a7, so that when white moves

Kd8-c8 black moves Bb8-a7. also, white can’t move either of his knights

because this will let black move Nh3 and release the position, so white

can only move his king.

so, as explained, white can kill Ba7 only if he can move an odd number of

moves with his king, and return to c8. this can be done in 19 moves:

Kd8-e7-f8:g7-f6-e5-d4-c3-b4-a4-a3-b4-c3-d4-e5-f6-e7-d8-c8.

and after black’s pawn g7 is gone, white can do it in 17 moves:

Kd8-e7-f6-e5-d4-c3-b4-a4-a3-b4-c3-d4-e5-f6-e7-d8-c8.

after each such sequence, black’s bishop is on a7, and can’t move to b8,

so black spare a pawn move.

black has 8 pawn moves to spare: h7-h6, h6-h5, h5-h4, h4:g3, g4-g3, g6-g5,

g5-g4, and g4-g3 again. as noted above, after the moves: h4:g3 and g4-g3

white must make the moves N:g3+ Kg1, Ne2+ kh1 so that black won’t release

the position.

so the sequence for the mate is:

white’s king 19 moves trip (including killing g7, meanwhile black moves

with his Ba7)

19. … h7-h6

20.-36. white king’s 17 moves trip

36. … h6-h5

37.-53. white king’s 17 moves trip

53. … h5-h4

54.-70. white king’s 17 moves trip

70. … h4:g3

71. N:g3+ Kg1, 72. Ne2+ Kh1

73.-89. white king’s 17 moves trip

89. … g4-g3

90. N:g3+ Kg1, 91. Ne2+ Kh1

92.-108. white king’s 17 moves trip

108. … g6-g5

109.-125. white king’s 17 moves trip

125. … g5-g4

126.-142. white king’s 17 moves trip

142. … g4-g3

143. N:g3+ Kg1, 144. Ne2+ Kh1

145.-161. white king’s 17 moves trip

162. … Ba7-b8

163. K:b8 Bg7 – somewhere,

164. R:f1+ Kg2, and finally 165. Nf3#

black can save his g7 pawn by moving g6-g5, and g7-g6, but

this means that black has pawns on g6 and g7, and white can make shorter

odd moves trips to h7. he can do it only after black moves h7-h6 ohterwise

black moves Nf4+ or Nf2+. now, white has an eleven moves trip:

Kd8-e7-f8-g7-h8-h7-g7-f8-e7-d8-c8.

so, the count is:

1.-19. white king trip, meanwhile black moves g6-g5 and g7-g6

19. … h7-h6

20.-30. 11 moves trip, … h6-h5

31.-41. 11 moves trip, … h5-h4

42.-52. 11 moves trip, … h4:g3

53. N:g3+ Kg1, 54. Ne2+ Kh1

55.-71. 17 moves trip, … g4-g3

72. N:g3+ Kg1, 73. Ne2+ Kh1

74.-90. 17 moves trip, … g5-g4

91.-107. 17 moves trip, … g4-g3

108. N:g3+ Kg1, 109. Ne2+ Kh1

110.-126. 17 moves trip, … g6-g5

127.-143. 17 moves trip, … g5-g4

144.-160. 17 moves trip, … g4-g3

161. N:g3+ Kg1, 162. Ne2+ Kh1

163.-179. 17 moves trip

179. … Bb8, 180. K:b8 Bg2-somewhere, 181 R:f1+ Kg2, 182. Ne3#

so, these are the whole 182 moves. another fabel’s masterpiece.

Dror.

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