# Rund um das Schachbrett

by Karl Fabel - Solutions

1 - numerous authors
Last move is -1. Kd1xNc1.

2 - Dr. Niels Høeg
Last 2 single moves are -1. Ba2xNb1 Nc3-b1 (-1. Ba2xRb1?? Rb2-b1+ would lead to retropat).

3 - Dr. K. Fabel
The different parts of the board display the following last moves:
up: -1. c7-c8=B+
left: -1. a2-a3+
right: -1. h2-h1=B+

4 - Dr. L. Ceriani
Bl. cannot retract g7-g6 while the wh. King is still behind the P barrier. Also, Wh. cannot retract g7xf8=N because g7xR/Qf8 leads to illegal check and g7xNf8 leads to bl. retropat.

There is only one way to avoid bl. retropat: last move is -1. Kg8xQh8, allowing -1 ... Q~-h8+.

5 - Dr. Niels Høeg
Last 3 single moves are -1. d5xe6 ep+ e7-e5 -2. d4-d5+.

This problem is the most economical presentation of an en-passant capture in (Type C) "Last move?" problems.

6 - N. Petrovic
Last 6 single moves are -1. d5xe6 ep+ e7-e5 -2. d4-d5 Ke6xpf6 -3. e5xf6 ep+ f7-f5.

7 - N. Petrovic
Last 7 single moves are: -1. d5xe6 ep+ e7-e5 -2. d4-d5+ Kg6xpf6 -3. g5xf6 ep+ f7-f5 -5. d3-d4

8 - H. August and H. Heimpel
Last moves are
n-1 ... f5-f4 +
n. g2-g4 f4xg3 ep +
.

This position has the shortest proof game (here 5 moves) of all positions with last 3 (and even 4 here) single moves completely determined.

9 - H. August & Dr. K. Fabel
A possible proof game leading to the diagram is: 1. d4 h5 2. h3 Nf6 3. Nc3 Ng4 4. hg4 Rh6 5. Rh3 Rb6 6. Rg3 Na6 7. Nf3 Nc5 8. dc5 a6 9. cb6 Ra7 10. ba7 h4 11. a8=Q h3 12. Qa7 h2 13. Qe3 h1=B 14. Nh2 a5 15. f3 a4 16. Kf2 a3 17. Na4. The last 16 single moves are completely determined.

10 - H. August
The last 54 single moves were: -1. Nf6-g4 h3-h2 -2. Qa4-a2 a2-a1=N -3. Qe8-a4 a3-a2 -4. e7-e8=Q a4-a3 -5. e6-e7 a5-a4 -6. e5-e6 a6-a5 -7. e4-e5 a7-a6 -8. e2-e4 e3xBf2 -9. Kg1-f1 e4-e3 -10. Be3-f2 e5-e4 -11. Bc1-e3 e6-e5 -12. Re3-d3 e7-e6 -13. Ne6-d8 d2-d1=B -14. Qd8-d4 d3-d2 -15. d7-d8=Q d4-d3 -16. d6-d7 c5xRd4 -17. Ra4-d4 c6-c5 -18. Ra1-a4 c7-c6 -19. a2xBb3 b4-b3 -20. d5-d6 b5-b4 -21. d4-d5 b6-b5 -22. d2-d4 d3xBc2 -23. f2-f3 d4-d3 -24. Be4-c2 d5-d4 -25. Bg2-e4 d6-d5 -26. Bf1g2 d7-d6 -27. g2-g3 Bg3-h4, and finally the whole position unlocks.

11 - Dr. K. Fabel
1. Nf3 a5 2. Nd4 a4 3. Nb3 ab3 4. a3 Ra4 5. Ra2 ba2 6. Rg1 ab1=N 7. Rh1 Nc3 8. Rg1 Nb5 9. Rh1 Na7 10. Rg1 b5 11. Rh1 Bb7 12. Rg1 Bd5 13. Rh1 Ba2 14. b3 h5 15. Bb2 h4 16. Bf6 h3 17. Bh4 Nf6 18. Qa1 Nh5 19. Qf6 Rf4 20. Qa6 e6 21. Kd1 Qg5 22. Kc1 Qg3 23. hg3 Bc5 24. gf4 Be3 25. Bg3 Ke7 26. Bh2 Kf6 27. g3 Kf5 28. Bg2 Kg4 29. Ba8 Nbc6 30. Kb2 Rb8 31. Ra1 Bb1 32. Bg1 h2 33. Kc3 Kh3 34. Kd3 Kg2 35. Ke4 Kf1 36. Kf3 Ke1 37. Kg4 Kd1 38. Kg5 f6 39. Kg6 Kc1 40. Kf7 Nd8 41. Ke8 Kb2 42. Ra2

13 - H. August and Dr. Karl Fabel
The black pawns captured 5 times, and the white pawns captured 3 times. If e5 didn't come from b2, then at least one of the pawns from the a-line or the b-line was captured by the black pawns, but none of those captures was on those lines. So e5 came from b2, which also implies that the white h-pawn promoted and got captured later. So h4xg3 can't be retracted until the h-pawn is unpromoted and back on h2 or h3.

Retract -1. .. Rc7-c8 -2. Ka8-b8 Ke8-d8 -3. Kb8-a8 Kf7-e8 -4. Ka8-b8 Kg6-f7 -5. Kb8-a8 Kg5-g6 -6. Ka8-b8 Kh4-g5 -7. Kb8-a8 Kh3-h4 -8. Ka8-b8 Kh2-h3 -9. Kb8-a8 Kg1-h2 -10. Ka8-b8 Kf1-g1 -11. Kb8-a8 Ke1-f1 -12. Ka8-b8 Kd1-e1 -13. Kb8-a8 Kc1-d1 -14. Ka8-b8 Kb2-c1 -15. Kb8-a8 Ka3-b2 -16. Ka8-b8 Ka4-a3 -17. Kb8-a8 Ka3xPa4 -18. Ka8-b8 Kb2-a3 -19. Kb8-a8 Kc1-b2 -20. Ka8-b8 Kd1-c1 -21. Kb8-a8 Ke1-d1 -22. Ka8-b8 Kf1-e1 -23. Kb8-a8 Kg1-f1 -24. Ka8-b8 Kh2-g1 -25. Kb8-a8 Kh3-h2 -26. Ka8-b8 Kh4-h3 -27. Kb8-a8 Kg5-h4 -28. Ka8-b8 Kg6-g5 -29. Kb8-a8 Kf7-g6 -30. Ka8-b8 Ke8-f7 -31. Kb8-a8 Kd8-e8 -32. Ka8-b8 Kc8-d8 -33. a3-a4 Rd8-d7 -34. a2-a3 Rd7-c7 -35. Bb8-d6 Rc7-d7 -36. Rd7-d5 and play forward 1. Rc7#.

14 - H. August
The position 65 moves ago was

From here, play forward: 1. Qh3 Nd5 2. a3 Bf5 3. a4 Bg4 4. e4 f5 5. e5 Nf6 6. exf6 e5 7. c3 e4 8. c4 e3 9. c5 e2 10. c6 e1=Q 11. a5 Qc3 12. a6 Qxc6 13. f7 Qd6 14. Ne4+ Qg3 15. Nf6 c5 16. Nd5 c4 17. Nf6 c3 18. Nd5 c2 19. Nf6 bxa6 20. Nd5 a5 21. Nf6 a4 22. Nd5 a3 23. Nf6 a2 24. Nd5 a1=B 25. Nf6 a6 26. Nd5 a5 27. Nf6 a4 28. Nd5 a3 29. Nf6 a2 30. Nd5 f4 31. Nf6 Be6+ 32. Ng4 Bb3 33. Be2+ and the diagram position is reached.

15 - Dr. L. Ceriani and Dr. K. Fabel
1. a4 c5 2. a5 c4 3. a6 c3 4. b3 d5 5. Bb2 cb2 6. Na3 Kd7 7. Nc4 Kc6 8. Ne5 Kb5 9. Ra5 Kb4 10. Rb5 Ka3 11. Nef3 Ka2 12. c3 d4 13. Qc1 e5 14. Kd1 e4 15. Kc2 e3 16. Kd3 g5 17. Ke4 g4 18. Kf4 d3 19. Qc2 dc2 20. h3 c1=R 21. Rh2 Ra1 22. Rh1 Kb1 23. Rh2 Kc1 24. Rh1 Bf5 25. Rh2 Bb1 26. d3 f5 27. Nd2 ed2 28. Nf3 Nf6 29. Kg5 Bd6 30. Kh6 Nd5 31. Kg7 Ne3 32. Kf7 h5 33. Kg7 Ra4 34. Kf7 Ba2 35. Rb6 d1=B 36. Kg7 Bc2 37. Kf7 Bcb1 38. Kg7 Nd1 39. Kf7 g3 40. Kg7 gh2 41. e3 h1=R 42. Be2 Nd7 43. Nh2 Nc5 44. Bg4 Ne4 45. Kf7 hg4 46. Kg7 g3 47. Kf7 gh2 48. Kg7 Re1 49. Kf7 Re2 50. Kg7 Rc2 51. Kf7 h1=R 52. Kg7 Re1 53. Kf7 Bh2 54. Kg7 Ng3 55. Kf7 Nh1 56. Kg7 Rah4 57. Kf7 Kd2 58. Kg7 Ke2 59. Kf7 Rc1 60. Kg7 Bc2 61. Kf7 Ra1 62. Kg7 Bab1 63. Kf7 Ra5 64. Kg7 Ba2 65. g3 Kf3 66. Rb4 Rb5 67. Kf7 Re2 68. Kg7 Bcb1 69. Kf7 Rc2 70. Kg7 Rc1 71. Kf7 Bc2 72. Kg7 Ra1 73. Kf7 Bab1 74. Kg7 Raa5 75. Ra4 ba6 76. Ra1 Ba2 77. Rc1 Bcb1 78. Rc2 f4 79. Re2 Bc2 80. Re1 Bab1 81. Rg1 Ra1 82. Rg2 Ba2 83. Kf7 Rc1 84. Kg7 Bcb1 85. Kf7 Rc2 86. Kg7 Re2 87. Kf7 Re1 88. Kg7 Rg1 89. Kf7 Bc2 90. Kg7 Bab1 91. Kf7 Ra5 92. Kg7 Ra1 93. Kf7 Ba2 94. Kg7 Rc1 95. Kf7 Bcb1 96. Kg7 Rc2 97. Kf7 Re2 98. Kg7 Ree1 99. Kf7 Ref1 100. Kg7 Bc2 101. Kf7 Bab1 102. Kg7 a5 103. Kf7 a4 104. Kg7 a3 105. Kf7 a2 106. Kg7 a1=R 107. Kf7 Ba2 108. Kg7 Rc1 109. Kf7 Bcb1 110. Kg7 Rc2 111. Kf7 Re2 112. Kg7 Ree1 113. Kf7 Bc2 114. Kg7 Bab1 115. Kf7 a5 116. Kg7 a4 117. Kf7 a3 118. Kg7 a2 119. Kf7 a1=R 120. Kg7 Ba2 121. Kf7 Rc1 122. Kg7 Bcb1 123. Kf7 Rc2 124. Kg7 Ke2 125. Kf7 Kd2 126. Kg7 Kc1 127. Kf7 Rce2 128. Kg7 Kd2 129. Kf7 Bc2 130. Kg7 Bab1 131. Kf7 Ra1 132. Kg7 Ba2 133. Kf7 Rc1 134. Kg7 Bcb1 135. Kf7 Rc2 136. Kg7 Kc1 137. Kf7 Rcd2 138. Kg7 Bc2 139. Kf7 Kb1 140. Kg7 Ka1 141. Kf7 Bab1 142. Kg7 Ka2 143. Kf7 Ka3 144. Kg7 Ba2 145. Kf7 Bcb1 146. Kg7 Rc2 147. Kf7 Rc1 148. Kg7 Bc2 149. Kf7 Ra1 150. Kg7 Bcb1 151. Kf7 Rc2 152. Kg7 Qd5 153. Kf6 Qf3 154. Kf7 Qe2 155. Kg7 Qd2 156. Kf7 Qc1 157. Kg7 Rce2 158. Kf7 Qd2 159. Kg7 Bc2 160. Kf7 Rc1 161. Kg7 Bcb1 162. Kf7 Rc2 163. Kg7 Qc1 164. Kf7 Rcd2 165. Kg7 f3 166. Kf7 Bc2 167. Kg7 Qa1 168. Kf7 Bcb1 169. Kg7 Rc2 170. Kf7 Rc1 171. Kg7 Bc2 172. Kf7 Bab1 173. Kg7 Ka2 174. Kf7 Red2 175. Ke7 Ree2 176. Kd7 Rfe1 177. Kc7 Rgf1 178. Kb7 Bg1 179. Ka7 R8h6 180. Rh2 Rb6 181. Rg2 Rh7 182. Ka8 Rhb7 183. Rh2 Rb8

19 - Dr. Karl Fabel
(a): Last 6 moves were: -1. Rf1-h1 f6xNe5 -2. Nf3-e5 Kh1-g2 -3. Ng1-f3 Kg2-h1.
(b): Start from the following position:

Before this position, black played 4 king moves at least. Now play forward:

1. b3 Kc5 2. Bb2 Kb4 3. Bd4 Ka3 4. Bc5 Kb2 5. Kg5 Kc1 6. Kg4 Kd1 7. Kg5 Ke1 8. Kg4 Kf1 9. Nf3 Kg2 10. Rb1 f6 11. Ne1 Kf1 12. Rb2 Kg1 13. Nf3 Kf1 14. Nd4 Ke1 15. Kg3 Kd1 16. Kg2 Kc1 17. Kf1 Kd1 18. Rg1 Kc1 19. Rh1 Kd1 20. Nf3 Kc1 21. Ng1 Kd1 22. Kg2 Ke1 23. Kg3 Kf1 24. Kg4 Kg2 25. Rg7 Kf1 26. Nf3 Kg2 27. Rhb1 d6 28. Ne1 Kf1 29. Ra2 Kg1 30. Rbb2 Kf1 31. Ra3 Kg1 32. Nf3 Kf1 33. Nd4 Ke1 34. Kg3 Kd1 35. Kg2 Kc1 36. Kf1 Kd1 37. Rg1 Kc1 38. Rh1 Kd1 39. Nf3 Kc1 40. Ng1 Kd1 41. Kg2 Ke1 42. Kg3 Kf1 43. Kg4 Kg2 44. Rg8 Kf1 45. Nf3 Kg2 46. Rhb1 d5 47. Ng1 Kh1 48. Rba2 Kg2 49. Rbb2 Kh1 50. Nf3 Kg2 51. Nd4 Kf1 52. Kg3 Ke1 53. Kg2 Kd1 54. Kf1 Kc1 55. Rg1 Kd1 56. Rh1 Kc1 57. Nf3 Kd1 58. Ng1 Kc1 59. Kg2 Kd1 60. Kf3 Ke1 61. Ke3 Kf1 62. Kd4 Kg2 63. Kc3 Kf1 64. Kb4 Kg2 65. Bd6 Kf1 66. Nf3 Kg2 67. Rf1 d4 68. Ng1 Kh1 69. Rbb1 Kg2 70. Rab2 Kh1 71. Rbe1 Kg2 72. Rbb1 Kh1 73. Ra2 Kg2 74. Ka3 Kh1 75. Kb2 Kg2 76. Kc1 Kh1 77. Ra3 Kg2 78. Rb2 Kh1 79. Rba2 Kg2 80. Kb2 Kh1 81. Rb1 Kg2 82. Kc1 Kh1 83. Kd1 Kg2 84. Ke1 Kh1 85. Rd1 Kg2 86. Rb2 Kh1 87. Raa2 Kg2 88. Bc5 Kh1 89. Rbb1 Kg2 90. Rbc1 Kh1 91. Rb2 Kg2 92. Rbb1 Kh1 93. Ba3 Kg2 94. Bb2 Kh1 95. Nf3 Kg2 96. Ne5 fe5 97. Rh1
There are 91 black king-moves in this sequence. So black played 95 king moves at least.

20 - T. R. Dawson
Retroplay: -1. Rf4-f5 Nf6-g8 -2. c4-c5 Ne4-f6 -3. c3-c4 Nc5-e4 -4. Nf6-d7 Nd7-c5 -5. Ng8-f6 Rf6-f7 -6. Nh6-g8 Rf7-f6 -7. c2-c3 Rf6-f7 -8. Nf7-h6 a5-a4 -9. Nh8-f7 Rf7-f6 -10. h7-h8=N Rf6-f7 -11. h6-h7 Rf7-f6 -12. h5-h6 Rf6-f7 -13. h4-h5 h5xg4 etc.
Letting Black start the retroplay is impossible because of the retro-opposition, so he has the move and wins easily with 1. .. Rc6 and white has no defense against Rc8#.

21 - Dr. Karl Fabel
White captures: d2xe3 and c5xb6. Black captures: fxg and a7xb6. The white a- and f-pawn promoted without capturing. The position unlocks after white has unpromoted a piece on a8, so black can take back a7xb6. The only piece that's available for unpromoting is the knight on f7.
Last moves could've been: -1. Rd6-c6 Nc6-b8 -2. g3-g4 Na5-c6 -3. Rc6-d6 Nc4-a5 -4. h4-h5 Nd6-c4 -5. Nd8-f7 Nf7-d6 -6. Rd6-c6 Rc6-c7 -7. h3-h4 Rc7-c6 -8. Nc6-d8 g6-g5 -9. Nb8-c6 Rc6-c7 -10. Na6-b8 Rc7-c6 -11. h2-h3 Rc6-c7 -12. Nc7-a6 b5-b4 -13. Na8-c7 Rc7-c6 -13. a7-a8=N Rc6-c7 -14. a6-a7 a7xb6 and the position unlocks.
White and black both need all the pawn move retractions they can do in this retroplay, so it's impossible to get this position with white to move.
Black can mate in 1 with 1. .. Re7#, so white can't win.

B - Dr. Karl Fabel
1. Qf1 Kb2 2. Qg1 Kb3 3. Qf1 Ka4 4. Qg1 Ka5 5. Qf1 Kb6 6. Qg1 Kc7 7. Qf1 Kd8 8. Qg1 Ke7 9. Qf1 Kf8 10. Qg1 Kg7 11. Qf1 Kh6 12. Qg1 Kh5 13. Qf1 Kg5 14. Qg1 Kf4 15. Qf1 Ke3 16. Qg1 Kd3 17. Qf1 Kd4 18. Qg1 Kc4 19. Qf1 Kb3 20. Qg1 Kb2 21. Qf1 Ka1 22. Qg1