Solutions

**210 - Bror Larsson**

Assume Wh. can still castle. Then the 2 bl. promoted Bs required 9 caps
to bring bl. pawns from f7 & h7 to b1 & c1. With wBf1 captured at home,
this accounts for all missing wh. units. Therefore, **Bl. last
move is not a capture** and Wh. did move his K or R just previously.
In conclusion, **Wh. cannot castle**.

Solution: **1. Tf1#** and not 1. 0-0??

**211 - Dr. Karl Fabel**

Bl. caps are a7xb6, bxc and wPf on its f-file. For balance, the wPg2
did promote on h8 after g6xh7. Other wh. caps are d2xc3, a2xb3xc4 and
bBf8 at home. This accounts for all captures.

The position unlocks by **(1)** unpromoting a wR on h8,
**(2)** resurrecting bl. QB through g6xBh7, **(3)**
reconducting this bB to c8, **(4)** retracting b7-b6 and
later b6xc5, **(5)** thus freeing wNa4 and then wBb1.

Unpromoting a wR requires that it uses the d1-a1-a3-b3-b5-a5-a7-b7-b8-h8
corridor. But there is a bR trapped in the corridor right now and the
only way to eventually unpromote a wRh8 is to assume that wKe1 did move,
so that the bRa1 can be freed. In conclusion, **Wh. cannot castle**.

Solution: **1. Tf1#** and not 1. 0-0??

**212 - Thomas Dawson**

Bl. last move could not have been made by his King, so that it can only
have been -1. d7-d5 or -1. f7-f5. But which one?

The wh. Pawns require all 10 captures (7 captures to get Pawns a2,
b2, c2 & d2 to the right, 3 captures to get f2, g2 & h2 to the left)
so that -1. d7-d5?? must be ruled out (or else the bl. QB from c8 could
not have been captured by a wP). Hence **last move was f7-f5**
and 1. g5xf6!! en-passant is legal,
allowing 2. f7# after any bl. move.

Here the well-known theme "a symmetrical-looking position has a non symmetrical solution" shows asymmetry in the past, instead of the future, of the position.

**213 - Thomas Dawson**

The 4 bl. caps have been b7xc6, c7xd6, e7xf6 & h7xg6.

The 6 wh. caps have been b4xa5, gxh, d2xe3xf4xg5xh6.

Wh. gxh must have been **g2xBh3** because this is the only
light-square capture by Wh.

Before retracting e7xf6 we must reconduct the bKB home. But this requires the retraction of c7xd6, which in turn requires the retraction of b7xc6, freeing the wPc7. This further requires that the bQB be reconducted on c8, which requires the retraction of g2xBh3, which requires that the wKB (and then the wKR) be reconducted home to f1 (and h1).

But at most one wh. unit can be uncaptured now, through h7xg6. So
that **the wKB was captured on g6** and **the wKR
is the Rook now on a1** !!
Hence wh. O-O-O is not legal anymore.

Mate in 2 is with 1. Kd2+ Kg2/Bg1 2. Nf4/Rxg1# and not 1. O-O-O??

**214 - Bengt Giöbel**

wQe5 is wPh2 promoted into a Q. If the wPh2 passed through square e7
on its way to promotion , then surely the bl. King had to move and cannot
castle anymore. Is there a way of keeping Bl. castling rights?

Only possibility of not disturbing the bl. K is through h2xg3xf4xe5xd6xc7. But this requires at least 5 caps, which is all what is available (considering that bQBc8 was captured at home). There is no difficulty with including the bPa7 in this account: it had to promote through (e.g.) a7-a4xNb3xRa2-a1=Q/N. Now, when wh. played c7-c8=Q, the bRb6 had to be on d8, shielding the bKe8 from the wQc8. But then, what did Bl. play then? He had no available move. e7-e6 had already been played to let the KBf8 be captured. Only units with possible moves were bKe8 and bRh8. One of them had to move and then castling is now forbidden.

Mate in 2 is with 1. Rxd7 2. Qb8# and Bl. cannot prevent this with 1 ... O-O.

**215 - Pentti Sola**

Bl. caps are b7xa6 & g7xh6. Hence bPe7 did not leave its column.

Then Wh. caps are cxd, g2xf3, h2xg3xf4 and a bP on e7 or e6. For balance,
wPb2 was promoted on b8.

So that Bl. last move is not -1. b7xa6??. Only remaining possibilities are -1. f7-f5 and -1. f6-f5. -1. f7-f5 allow further retracting -1 ... Nf5-e7+ while -1. f6-f5?? leaves Wh. in retropat (-1 ... Nf5xPe7+?? and bBd8 is entombed).

Hence **last move is -1. f7-f5** and forward **
1. e5xf6 ep+!!** is legal, leading to 1 ... Kxe8 2. Rg8#

**216 - Thomas Dawson**

Bl. only cap. is e7xPd6. Wh. caps are g2xPh3, a6xb7 & b4xc5. Is Wh.
O-O legal?

No uncapture is allowed right now. The only way to open the position without breaking Wh. O-O is to interpose the wQ on c3 so that the bNb4 can be freed. The wQ can reach c3 via the a6-a7-b8-c7-d8 corridor.

Retract

-1. Rc7-c6 Qa7-a6

-2. Rc6-c7 Qb8-a7

-3. f7-f6 (only waiting move) Qc7-b8

and Bl. is retropat.

If Bl. were to move in the diagram position, the f7-f6 tempo would
be enough to allow the wQ through c7. But there is no way to lose/win
one tempo and swap side-to-move. Because of this retro-opposition on
c7, we see that **Wh. cannot castle anymore**.

Forward mate is with **1. Nd3++ Kxc2 2. Qxc4#** and not
1. O-O+??

**217 - Dr. Niels Høeg**

Here, castlings are mutually
exclusive. To see this assume, by way of contradiction, that both
sides may castle. Then wQ and wQR have been captured by bNs (together
with the wQB) and wQf4 is the promoted wPf2 on c8 or b8. So that bl.
caps f7xg6, b7xa6, e7xd6 consumed the 2 wNs and the wBf1. There are
now three cases:

**wPf2 promoted on c8**. Then it went through d6xc7 before bl. could play e7xd6 and release his Bf8 and Rh8, so that the wPf2 captured the bQ and both bNs to reach c7, and the wPg2 captured the bR on light-squared h3. As a consequence, when bl. finally plays e7xNd6 & f7xNg6, letting the Rf8 reach h3 for capture, wPg2 and then bPb7 & bBc8 are still home and wh. has no tempo move (his Q and QR have already been captured).**wPf2 promoted on b8****through c7xb8=Q**. Then the wPf2 had to go through d6xc7 and we can borrow from previous case to see that the capture was c7xBb8. But then there is no way the Bf8 could have reached b8 with a wP already at c7.**through b7-b8=Q**. When we play n. b7-b8=Q, the wPf2 has already captured 4 bl. units and the bPb7 is already on a6, so that g2xh3 and f7xg6 already took place. The bBc8 must be on c8, as the only possible shield between bKe8 and wQb8 so that the only move for Bl. is n ... c7-c6 before Wh. removes his wQ. But then Bl. has no last move because only n-1 ... c7-c6 could have been played just before n. b7-b8=Q.

Mate in 3 is with **1. Qxd6!!** (threat. 2. Rf1 & 3.
Rf8#) Bb7 **2. O-O !!** (not 2. Rf1??) forbidding the now-illegal
defense 2 ... O-O-O??, and allowing 3. Rf8#.

**218 - Pehr Törngren**

Wh. caps are e2xBd3 & h2xg3xf4xe5xd6xc7. Bl. caps are h7xBg6 and, for
balance, a3xNb2 for promotion of bPa7 on b1.

If we assume Bl. may still O-O-O, then the position unlocks by retracting f7-f5, so that h7xBg6 is not an impossible check to the bK. We can now reconduct the wBg6 to f1, retract e2xBd3, reconduct the bBd3 to c8, retract d6-d7 and then d6xc7. But then we see that, because we retracted f7-f5, the bKR (once it is uncaptured) can never be reconducted on h8 without disturbing the bK.

There is no other possibility, in particular no wh. or bl. unit (except
the bRa8) may be interposed on f7, allowing the retraction of h7xBg6.
Thus **Bl. O-O-O is not legal**.

Mate in 3 is with 1. Rh7 Bxc7 (or 1 ... Kf7/d7 2. Rhxg7+ etc) 2. Rhxg7 ... (2 ... O-O-O??) 3. Bxd6#

**220 - Dr. Niels Høeg**

Bl. caps include wBc1 at home so that bPf2 went straight from f7 and
wPf3 is from g2. wBg1 has been promoted on b8, accounting for at least
5 caps by wPs. bPh7 could not have been promoted on g1 because we must
retract g2xf3 before extracting the wBg1. The bK entered the 1st rank
via h3 & g2. Position unlocks by inserting something on b1, to let the
wRc2 reach c1, then the wK out through c2.

The unlocking process require at least 11 waiting moves by Bl. This
can be obtained by uncapturing a bPa3 and a bPh3. Retract:

-1. Ka1-b1 Nc6-b8

-2 ... Ne5-c6

-3 ... Ng6-e5

-4 ... Nf4-g6

-5 ... Nh3-g6

-6 ... Nf4xPh3

-7 ... Ng2-f4

-8 ... Ne3-g2

-9 ... Nb6-a4

-10 ... Nc4-b6

-11. Ka1-b1 Na3-c4

-12. **b4-b3** Nb1xPa3

-13. **b5-b4** Rc1-c2

-14. **a4-a3** Kc2-d1

-15. **a5-a4** Kd3-c2

-16. **a6-a5** Qd1-e1

-17. **d6-d5** Qa4-e1

-18. **d7-d6** Re1-c1

-19. **h4-h3** Nd1-e3

-20. **h5-h4** Na3-b1

-21. Kb1-a1 Nc4-a3+

-22 ... Ke4-d3

-23 ... Ne5-c4

-24 ... Nd3-e5

-25 ... Nc1-d3

-26 ... Qa5-a4

-27 ... Ne3-d1

-28 ... Nd5-e3

-29. Kc2-b1 Nd3-c1

-30. **h6-h5** Ra1-e1

-31. **h7-h6** Rb1-f1

-32. Kd1-c2 Nc1-d3+ and the position unlocks just when Bl. has no more
retro-tempi. Black could not retract one more pawn move on files a or
b because there has been a promoted wBb8.

In the diagram position, assuming Wh. played last would have required
one more retro-tempo (because Knights cannot lose one tempo) which is
impossible. Thus **Bl. played last** and Wh. wins through
1. Rc1+!! Kxa2 2. Nc6 fxe1=Q+ 3. Rxe1 ... 4. Nb4#, not Bl. through 1
... bc2#??.

**221 - Harold Cross**

Bl. caps are a3xb2, g3xf2 & h4xg3. Wh. only cap is axb. For balance,
the wPh2 had to promote on h8. Position unlocks by reconducting bNh4
on c1, thus freeing the wNb1 that can be unpromoted on h8. When the
promoted wPh2 is reconducted past h4, we can unlock by retracting bPh4xg3.

Retract

-1. Ng6-h4 Rc1-d1

-2. Nf4-g6 R..

-3. Nd3-f4 R..

-4. Bh3-f1 Rd1-c1

-5. Nc1-d3 Nc3-b1

-6. Bf1-h3 Nd5-c3

-7. B.. Nf4-d5

-8. B.. Ng6-f4

-9. B.. Nh8-g6

-10. B.. h7-h8=N

-11. B.. h6-h7

-12. B.. h5-h6

-13. B.. h4-h5

-14. Bf1-h3 h2-h4

-15. h4xg3 etc.

Starting with a Wh. retraction would lead to an unsurmountable retro-opposition
on h4 between wP and bB. It is not possible to swap side to move. Therefore
**Bl. played last** and Wh. wins with 1. Nc3!! b1 2. Rxb1#
(not Bl. with 1 ... Bg2#??)

**222 - Edgar Fielder**

Bl. caps are bxc & axbxc. Wh. caps are e2xd3, bBf8 & (for balance) fxexdxcxb
for promotion on b8. The S-W cage unlocks by retracting e2xd3. Before
this, we have to uncapture the wBf1 through b7xBc6, so that we first
have to uncapture bQ and bQB and unpromote wPf2 on b8. This can be done
by unpromoting the wQa4, so that Bl. cannot castle. Further, we need
a very quick maneuver to avoid Wh. retropat.

Put bK on g8, bR on c8 & wQ on b5 and retract

-1. Rd8-c8 Qb8-b5

-2. Re8-d8 b7-b8=Q

-3. Rf8-e8 c6xQb7

-4. Qc8-b7 d5xBc6

-5. Qd8-c8 e4xNd5

-6. Bb7-c6 e3-e4

-7. Bc8-b7 h5-h6

-8. c6-c5 h4-h5

-9. b7xBc6

and Wh. retropat is avoided just in time. (It is not possible to retract
h2-h4 with wKR out).

**Black did already O-O in the past !!**

**223 - Harold Cross**

Wh. caps are axb & bxc. Bl. caps are axb & dxe. Wh. cannot retract c2-c3
because of his wBd1. The cage unlocks by pushing the three Rooks one
square to the right and inserting something on e1 so that the wBd1 can
be extracted. Only a wN, uncaptured by bPdxe can go to e1.

Retract:

-1. d2-d4!! d5xNe4

-2. Ng5-e4 Rg2-g1

-3. Nf3-g5 Rg1-f1

-4. Rf1-e1 d7-d6

-5. Ne1-f3 h7-h6

-6. Bc2-d1 Kd1-c1

-7. Bd3-c2+

and everything unlocks just in time to avoid bl. retropat.

We see that last move must have been **-1. d2-d4!!**
(and not -1. d3-d4??) so that -7. Bc2+ can be retracted later. Therefore,
the en-passant capture is legal.

**224 - Dr. Niels Høeg**

Last moves were **-1. Ba2xNb1 Nc3-b1**.

-1 ... Nc3xRb1?? fails because unlocking the SW cage requires that the wK goes to b1, letting the bB out.

**225 - Dr. Niels Høeg**

Last moves were **-1. d5xe6ep+ e7-e7 -2. d4-d5+**.

**226 - Dr. Niels Høeg**

Bl. did not capture. All wh. caps are by Ps: exd, fxe, gxf, hxg & two
cross-captures *a-b* or *b-c* to get a Pb7 beyond the
barrier of bPs. With these constraints, last 13 singles moves are forced:

**-1. Rd8-d7+ d7-d6 -2. f5xe6 ep+** (e5-e6+?? bl. retropat)
**e7-e5 -3. f4-f5+ Kd6-c7 -4. b5xc6 ep+ c7-c5 -5. b4-b5+ Ke6-d6
-6. g5xf6 ep+ f7-f5 -7. g4-g5+** and Bl. avoids retropat.

**Three** en-passant captures in retro-play !!

**319 - Valerian Onitiu**

Bl. caps are exd, hxg & gxf. Bl. is under threat of retropat for he
cannot retract exd while the wPe7 is up there. Position unlocks by unpromoting
the wQ on e8, so that there will be a shield on d7. But we need to uncapture
a bPa5 to get bl. retro-tempi.

Necessarily, last moves were:

-1. Qb4-f4 d4-d3

-2. Qa5-b4 d5-d4

-3. Qb5xPa5 a6-a5

-4. Qe8-b5 a7-a6

-5. d7xRe8=Q etc.

So that wh. retracts **-1. Qb4-f4** and mates in 1 with
**1. Qe4#**.

**321 - Dr. Niels Høeg**

Black retracts **-1. Ke7xPd6!!** allowing forward h#1 with
**1. Kf8 Nh4#**.

Retracting -1. Ke7xPd6 puts the bK under a **quadruple**
check (!!), but this is explainable via -1 ... e5xd6ep+++ -2. d7-d5
N..-b1+. By contrast, retracting only -1. Ke7-d6?? would allow the forward
h#1 but this puts the bK under an impossible double check by Re4 and
Nightrider b1.

**322 - Dr. Julio Sunyer**

Retract -1. Kg6xRh5 Rh8xQh5 and play forward 1. O-O Qh7#

**323 - Hans Schmitz**

Retract -1. Bb2-f6 c4xd3ep and play forward 1. Kf6 d5#.

**324 - Edgar Fielder**

Retract **-1. d7xNe6 Ng7-e6** and all 16 Bl. units are
retro-stalemate when they were previously free !!

**325 - Herbert Hultberg**

**(a)** Wh. retracts **-1. f5xg6 ep** and
plays **1. Ng7#**

**(b)** Bl. retracts **-1. c3-c2** and plays
**1 ... b1=N#**

**326 - Thomas Dawson**

Bl. used 7 caps to move his Ps to the West. Additionally, wPa2 was captured
on its file. Only wh. cap is f/hxBg3/5. Wh. did just play Qf4+ with
no capture.

There are five possible last moves:

-1. Qc4-f4+, then -1 ... Bb3-a4!! and forward 1. Rxc5#,

-1. Qd4-f4+, then -1 ... Qd3-h7!! and forward 1. Nxe3#,

-1. Qe4-f4+, then -1 ... Qh1-h7!! and forward 1. Rxg5#,

-1. Qe5-f4+, then -1 ... Qf5-h7!! and forward 1. fe6#,

-1. Qd6-f4+, then -1 ... Rd7-c7!! and forward 1. Ne7#.

**327 - Thomas Dawson**

All bl. caps are by P: c7xb6, dxcxb & h7xg6. Wh. caps are f6xe7 and
axb so that wPa2 could get captured. Perhaps wPc2 was promoted on c8.

There are only four possible last moves:

-1. Nf2-h1, then -1 ... h7xQg6!! and forward 1. Kh4 g3#,

-1. Bf2-g1, then -1 ... h7xRg6!! and forward 1. Bc2 g4#,

-1. Nf7-h8, then -1 ... h7xBg6!! and forward 1. Kg4 Rxa4#,

-1. Qc8-b8, then -1 ... h7xNg6!! and forward 1. e5 Qf5#.

**334 - Gustav Jönsson**

Retract

**-1. c5xb6ep** forcing **-1 ... b7-b5**

**-2. Rb6-a6** forcing **-2 ... b4-b3** (-2
... Kb8-c8??)

**-3. Ke6-e7** forcing **-3 ... O-O-O**

**-4. e7xf8=B**

and forward **1. e7xf8=Q#**.

**336 - Charles Kemp and Thomas Dawson**

Retract

-1. Kf7xNe7 Nc8-e7

-2. Kg8xRf7 Rc7-f7

-3. O-O Rd7-c7

and Bl. has no legal retraction (because his O-O must be legal).

A symmetrical-looking position has a non-symmetrical solution.

**337 - Bror Larsson**

Retract

-1. b3x**Q**a2 Qg2-a2

-2. c4x**R**b3 Rh3-b3

-3. d5x**B**c4 Bb5-c4

-4. e6x**N**d5 Nf6-d5

-5. f7x**P**e6 e5-e6

and Bl. is retropat.

Uncaptures of Q/R/B/N/P.

**338 - Charles Kemp**

Retract

-1. Kf7xRg8 Rd2-d8

-2. Ke7xQf7 Qc4xPf7+

-3. Kd8xNe7 Nd5xPe7+

-4. Kc8-d8 Rg3-g8

-5. Rd8xNf8 Nd7-f8

-6. O-O-O Kc5-c6

and Bl. is retropat.

**340 - Dr. Julio Sunyer and George Alvey**

Bl. caps are a7xb6 and exf. Wh. caps are axb, g2xh3, b-c cross-captures
and hxg for Rook-promotion on g8. The bl. King entered the corridor
through a3. Then all 3 wRs had to be shuffled inside the corridor, through
g2. Other wh. units were easier to insert. During all this time, the
bl. King had to play waiting moves, except when the wRs were just entering
and when he had to wait sitting on g2. For these moments, the e7-e6xf5-f4
maneuver allowed 3 tempi.

Here is a proof game with minimal number (only 96 !!) of bK moves:

1. h4 c5 2. h5 Qb6 3. h6 Kd8 4. hxg7 Kc7 5. Nc3 Nf6 6. Na4 Qb3 7. Nb6
axb6 8. cxb3 Ra3 9. g8=R Bg7 10. Qc2 h5 11. Qf5 Ne4 12. Kd1 Bc3 13.
Kc2 Ba5 14. Rh4 c4 15. Rf4 c3 16. Kd3 c2 17. Nf3 Nc3 18. bxc3 h4 19.
b4 h3 20. Bb2 h2 21. Ke3 Rh3 22. gxh3 Kc6 23. Bg2 Na6 24. Rh1 Nc5 25.
Bf1 Kb5 26. Bc1 Ka4 27. Ne5 Nb3 28. Nd3 Na1 29. Rh8 Rb3 30. Nb2 Ka3
31. axb3 Ka2 32. Qb5 Kb1 33. Nd3 Ka2 34. Ba3 Kb1 35. Nb2 Kc1 36. Nc4
Kd1 37. Ne5 Ke1 38. Nf3 Kd1 39. Ng1 Ke1 40. Bg2 Kd1 41. Bd5 Ke1 42.
Qa4 Kf1 43. Nf3 Kg2 44. Rb1 **e6** 45. Rb2 Kf1 46. Nd4
Kg1 47. Ra2 Kf1 48. Bg2 Ke1 49. Bf1 Kd1 50. Rg4 Ke1 51. Rg1 Kd1 52.
Rh1 Ke1 53. Nf3 Kd1 54. Ng1 Ke1 55. Bg2 Kd1 56. Be4 Ke1 57. Bf5 Kf1
58. Nf3 Kg2 59. Rb1 **exf5** 60. Rbb2 Kf1 61. Nd4 Ke1 62.
Kf3 Kd1 63. Kg2 Kc1 64. Kf1 Kd1 65. Rg8 Kc1 66. Rg1 Kd1 67. Rh1 Kc1
68. Nf3 Kd1 69. Ng1 Kc1 70. Kg2 Kd1 71. Kf3 Ke1 72. Ke3 Kf1 73. Kd3
Ke1 74. Kc4 Kf1 75. Rb1 Kg2 76. Bc1 Kf1 77. Qa3 Kg2 78. Qb2 Kf1 79.
Ra4 Kg2 80. Qa3 Kf1 81. Rb2 Kg2 82. Ra2 Kf1 83. Bb2 Kg2 84. Kb5 Kf1
85. Nf3 Kg2 86. Rb1 **f4** 87. Bc1 Kf1 88. Ne5 Kg1 89.
Ng4 Kf1 90. Ne3 Kg1 91. Nf1 Kg2 92. Bb2 Kg1 93. Rd1 Kg2 94. Bc1 Kg1
95. Qb2 Kg2 96. Qb1 Kg1 97. Ba3 Kg2 98. Qb2 Kg1 99. Rb1 Kg2 100. Qc1
Kg1 101. Qe1 Kg2 102. Rd1 Kg1 103. Rb2 Kg2 104. Rbb1 Kg1 105. Bc1 Kg2
106. Ra2 Kg1 107. Ka4 Kg2 108. Ka3 Kg1 109. Kb2 Kg2 110. Ra4 Kg1 111.
Ka2 Kg2 112. Ba3 Kg1 113. Kb2 Kg2 114. Kc1 Kg1 115. Rb2 Kg2 116. Ra2
Kg1 117. Kb2 Kg2 118. Rb1 Kg1 119. Qd1 Kg2 120. Kc1 Kg1 121. Bb2 Kg2
122. R4a3 Kg1 123. Ng3 Kg2 124. Nh5

**344 - Thomas Dawson**

Wh. does not need a Queen to mate in 1: **1. Nc3#** is
already possible. But retro-analysis of the position shows Bl. is
retropat.

Indeed 6 Bl. caps are e7xf6 & h7xg6xf5xe4xd3xc2 (which will account for all captures once a wQ is added). Wh. caps are axb, bxa, cxb, bxa for explaining the position of wPa6 & a7. Bl. last move cannot have been -1. Ka3-a2 because this requires -1 ... e7xf8=B+, one capture too many, nor -1. Ka1-a2 because this requires -1 ... Rb2-b1+ -2. Ka2-a1 Rb1-b2+ (or -2. Kb1-a1 Ra2-b2+ -3. Kb1-a1 etc.) and there is no way out of this retro-perpetual.

Solution is **add a wQe8!!** and then it is possible
to retract -1. Ka3-a2 e7-e8=Q+ without too many wh. caps.

**618 - Nikita Plaksin**

Position is explained by starting from:

and playing forward 1. **b3** Ra7 2. Bb2 Rf1 3. Be5 Ka3
4. Bd6 Kb2 5. Rg1 Kc1 6. Rh1 Kd1 7. Rg1 Ke2 8. Rh1 Rb1 9. Rg1 Rb2 10.
Bb1 Ra2 11. Rh1 Ra3 12. Ba2 Ra8 13. Rb1 Ra7 14. Rb2 Kf1 15. Kf3 Kg1
16. Ke2 Kh1 17. Kf1 Ra8 18. Rb1 Ra7 19. Re1 Ra8 20. Re2 Ra7 21. Ke1
Ra8 22. Kd1 Ra7 23. Kc1 Ra8 24. Kb2 Ra7 25. Bb1 Ra2 26. Kc3 Rb2 27.
Ba2 Rb1 28. Kd3 Rf1 29. Ke4 Ra8 30. Kf4 Ra7 31. Kg5 Ra8 32. Kh6 Ra7
33. Kg7 Ra8 34. Kf8 Ra7 35. Ke8 Ra6 36. Kd8 Ra8 37. Kc8 Ba7 38. Kb7
Rg8 39. Re1 Rg7 40. Rb1 Rg1 41. Rb2 Rf1 42. Bb1 Re1 43. Ra2 Bb8 44.
Ra3 Kg1 45. Ba2 Rb1 46. Kc8 Rb2 47. Bb1 Ra2 48. Kd8 Rb2 49. Qe2 Ra2
50. Bf4 Kh1

Thus, the last pawn or capture move has been **b2-b3**,
at least 49.5 moves ago. The fifty
move rules applies !

**Solution**: Mate in 3 starts with a capture:
**1. Rxg6 Rg8+ 2. Rxg8 ~ 3. Qe1#**, and not 1. Qd/e/f1+??
draw!!

**619 - André Hazebrouck**

The position requires that wPf2 promotes to f8 after e.g. Wh: axPb,
dxe, hxPg; Bl: axPb, fxe, hxPg, or that wPh2 promotes to h8 after e.g.
Wh: axPb, dxe, fxg; Bl: axPb, fxe, hxPg. In all cases, Bl. O-O is forbidden.
Meanwhile, the 3 other castlings are legal.

**Wh. mates in 5 with 1. Qc7** (threat. Qxe7#) Qxh1+
2. Kd2 Qc/d/e1+ 3. RxQ Kf8 (O-O? illegal!) 4. Qxe7+ and mate.

1. Qg7? fails on 3 ... O-O-O!! and Bl. cannot mate with 1... Qc2/Qg2?
which fail on 4. O-O / O-O-O !!

**620 - Josef Haas**

wBf1 has been captured at home and wBa4 is a promotee.Retract
**-1. Rb3xBb1** and now Bl. O-O-O is forbidden.

Indeed, Bl. cannot retract -1 ... b2-b1=B+ or -1 ... c2xb1=B+ or -1 ... Rf5xb5+ (too many captures) so that what has been played is -1 ... Rf5-b5+ -2. b5xa6+. There, the wBa4 promotion took place on a8, forbidding Bl. O-O-O.

Forward mate is then **1. Kxg7 ~ 2. Rf8#**.

(Other attempts at breaking Bl. O-O-O fail: -1. Bf2xBe1?? and Bl. can still O-O-O; -1. Kh7xPg6?? leads to an illegal position.)

**631 - Janko Furman**

**(a)** Bl. Ps g2 & h2 used two captures to reach their
tangled position. The 3rd bl. cap is e3xf2. Wh. used two cross-captures
on the King side (f/g or g/h), two cross-captures (axb, b2xa3) on the
Queen side, and c4xd5 before the bPc7 could promote to c1. All captures
are accounted for.

**If Bl. O-O-O is legal, then** the only way to avoid
Bl. retropat is to assume that **the last move is e2-e4**,
so that e3xf2 can be retracted. Thus, it is possible to play 1. d4xe3
ep if the en passant capture is
validated *a posteriori*.

**Solution**: 1. d4xe3 ep Ne5 2. O-O-O Rc4# (and not 1.
d4xe3 ep Nc5 2. Rd8?? Re4# because then 1. d4xe3 is not legal)

**(b)** Here wh. caps are the same Qside and Kside cross-captures
plus cxPd. Bl. did just play. If Bl. O-O-O is still legal, then the
last move must have been -1. c7-c5. Again, en passant capture is possible
if it is validated *a posteriori*.

**Solution**: 1 ... d5xc6 ep 2. O-O-O Ne7# (and not 1 ...
d5xc6 ep 2. Rd8?? Nc7# because then 1... d5xc6 is not legal)

**632 - Aleksandr Kislyak**

Position unlocks with the retraction of b2-b3. So that wBd8 is wPa2
promoted on b8 after axb. 2nd wh. cap. is bBf8 at home. Bl. caps are
bxc, c7xd6, h3xg2 for promotion of bPh7 and original wBc1. For balance
bPf7 had to be promoted.

Retract -1. Ne5-c4 Nd3-b2 -2. Nc4-e5 Nf4-d3 -3. Ne5-c4 Ng6-f4 -4. Nc4-e5 Nf8-g6 -5. Ne5-c4 f7-f8=N -6. Nf3-e5 f6-f7 -7. Ne1-f3 f5-f6 -8. e2-e1=N f4-f5 -9. e3-e2 f3-f4 -10. f4xBe3 Bd4-e3 -11. f5-f4 Bb2-d4 -12. f6-f5 Bc1-b2 -13. f7-f6 b2-b3 -14. Nb3-a1 h2-h3 -15. N~-b3 and everything unlocks.

It is not possible to give Bl. the move because the wPs e4, f3 & g3
cannot be further retracted. They had to give way to bPh3xg2, promoted
bBg1 and wKR. Thus mate in 1 is with **1. Nb2xc4#** and
not Nc4xb2#.

**633 - Jan Knöppel**

Retract **-1. Kd3-c4 !!** and now Bl. must choose between
the following possible retractions (-1 ... d5xPe4+ is illegal):

-1 ... d5xQe4+ -2. Qe7-e4+ and forward 1. Qh7#,

or -1 ... d5xRe4+ -2. Nb5-c7 and forward 1. Nd6#,

or -1 ... d5xBe4+ -2. Bf3-e4+ and forward 1. Bg4#,

or -1 ... d5xNe4+ -2. Bh2-g3!! and forward 1. Nd6#,

or -1 ... e5-e4+ -2. Ne6-c7 and forward 1. Ng7#.

**634 - Marko Klasinc and Matjaz Zigman**

Retract -1. Rh5-h1 c7-c6 -2. h2xPg3 g4-g3 -3. Rc5-h5 g5-g4 -4. Nd5-e7
~ -5. Ne3-d5 ~ -6. Nd1-e3 Qb1-a2 -7. Kf1-e1 Qc1-b1 -8. Kg1-f1 Ka2-a3
-9. ~ a3xRb2 -10. **Rb1-b2+** a4-a3 -11. Ne3-d1 Qa3-c1+
-12. Rf1-b1 Qb4-a3 -13. Rf5-c5 Qb8-b4 -14. Ba3-f8 ~ -15. Bc1-a3 ~ -16.
b2-b3 b3xNc2 so that the last move of the captured R was Rb1-b2+ and
its first was O-O.

**664 - André Hazebrouck**

Retract: -1. Nd5-c7 Rc7-d7+ -2. Nf4-d5 Nf8-e6 -3. Nh3-f4 Ne6-f8 -4.
Ng1-h3 Nf8-e6 -5. Nf2-d1 Ne6-f8 -6. Nh3-f2 Nf8-e6 -7. g2-g1=N Ne6-f8
-8. g3-g2 Nf8-e6 -9. g4-g3 Ne6-f8 -10. g5-g4 Nf8-e6 -11. g6-g5 Ne6-f8
-12. Ng1-h3 Nf8-e6 -13. g2-g1=N f7-f8=N -14. g3-g2 f6-f7 -15. g4-g3
f5-f6 -16. g5-g4 g4xBf5 -17. Bc8-f5 g3-g4 -18. d6-d7 g2-g3 -19. R~-c6
Nc6-a7 and everything unlocks.

Bl. cannot be given the move. 1 Nc8# and not 1 ... Nxb2#??

**666 - Aleksandr Kislyak**

1. b3 h5 2. a4 h4 3. a5 h3 4. Ra4 e6 5. Rh4 b5 6. a6 Bb7 7. axb7 a5
8. e4 a4 9. Nc3 a3 10. Na4 a2 11. Ne2 a1=B 12. Nf4 Be5 13. Rg1 c5 14.
Bb2 c4 15. Ba1 c3 16. Nb2 cxb2 17. c4 Ne7 18. c5 Nc8 19. c6 Bfd6 20.
Ke2 b1=Q 21. Kf3 Qd3 22. Kg4 Qg3 23. hxg3 h2 24. Bc4 Ke7 25. Kg5 bxc4
26. Qh5 c3 27. Qh7 c2 28. Qg8 h1=R 29. Rh7 Rh6 30. Nh5 c1=N 31. Rh1
Ne2 32. Rh2 Nf4 33. gxf4 f5 34. fxe5 Rf6 35. exf6#.

**Q/R/B/N Ceriani promotions** in shortest proof game,
from a time where dual-free SPGs where still quasi-unknown.

**667 - Wolfgang Dittmann**

Retract **-1. g5-g6 Kd8-e8 -2. g4-g5 Ke8-d8 -3. g3-g4 Kd8-e8 -4.
Kg2xBh1 h2-h1=B+ -5. Kh3-g2 Ke8-d8 -6. Kg2-h3 Kd8-e8 -7. Kh3-g2 Ke8-d8
-8. Kg2-h3** and now Bl. may not retract Kd8-e8 because this
would imply three-fold repetion and draw.

The same motivation exaplins the following moves: **-8 ... Ra8-a7
-9. b5xa6 ep. a7-a5 -10. Kh3-g2 -17. Kg2-h3 Ra8xNb8 -21. Kg2-h3 Ke8xNd8
-22. Ne6xNd8** and forward **1. Nc7#**.

**668 - Boris Ostruh and Marko Klasinc**

Retract **-1. Ng2xBe1**. Now Wh. could retract Bh2-g3 and
mate forward with Rg4-g3# if the Ne4 moves. **-1 ... ~ -2. Kh1xNg1
~ -3. Bh2-g3 ~** and eventually Bl. is obliged to retract a P
move to avoid draw by fifty moves rule. Observe that, because Wh. has
no choice of last move, Bl. has all the responsability for avoiding
draw. **-51. Bh2-g3 a3-a2 -101. Bh2-g3 a4-a3** etc.

Once bP a7, c7 and f7 are back home, Bl. can use his e3 pawn:
**-601. Bh2-g3 f7-f6 -602. Bg3-h2 Nf5-~ -603. Bh2-g3 N~-e4**
so that **-801. Bh2-g3 e6-e7**. Now Bl. must uncapture
wh. units (wPs are best) and free them in the slowest possible way:
**-851. Bh2-g3 Rb7xBb8 -900. Bg3-h2 Nd7-c5 -901. Bh2-g3 Qh8xBd8
-950. Lg3-h2 Rb6-b7 -951. b7-b8=B -1000. Bh2-g3 Rb5-b6 -1001. b6-b7
-1201. b2-b3 -1250. Bg3-h2 N~-d7 -1251. d7-d8=B Rd6-~ -1451. d3-d4**.

Bl. can also unpromote: **-1500. Bh2-g3 a2-a1=N -1700. Bh2-g3
a6-a5 -1750. Bh2-g3 c2-c1=B -1900. Bh2-g3 c5-c4 -1950. Bh2-g3 b7xPa6
-2000. Bh2-g3 d6xPc5 -2049. Bg3-h2 Rc3-c4 -2050. c4-c5 -2150. c2-c3
-2200. a5-a6 -2350. a2-a3**.

Eventually, Bl. must allow the retraction of f3-f4, unlocking the
cage: **-2399. Bh2-g3 Bc6-f3 -2400. f3-f4** and forward
**1. Ng2-f4#**.

**669 - Wolfgang Dittmann**

Wh. cannot retract once and play 1. O-O right now. Rather **-1.
Rh4xQh1 Q~-h1+ -2. Rb4xBh4 B~-h4+ -3. Rb1xBb4 B~-b4+ -4. Ra1-b1**
and forward **1. O-O-O**. Observe that -1. Rh4xRh1?? fails
on -1 ... Rh2-h1 -2. Rb4xBh4 .. -3. Rb1xBb4 **Rd2-h2+!**.

**670 - Andrei Frolkin**

Retract **-1. Qa6-a7# Kc7-b8 -2. a7-a8=N+ Kd6-c7 -3. c7-c8=N+**.

Now bl. 3 caps are axb, d7xc6 and c3xb2; wh. 7 caps are f6xe7, gxfxe7, hxgxfxe7 for promotion of wPs f2, g2 & h2 on e8, and exd for promotion on d8. wPd2 also promoted to d8. Only the 5 wNs can be unpromoted before we unlock the position with the retraction of e7-e6, Bc8-.. and d7xc6.

All **seven** wNs are promotees !!

**673 - Boris Ostruh and Marko Klasinc**

Retract **-1. Ba8xRh1 Na2xRc1 -2. Lg2xRa8 Rf8xRa8 -3. Rb8xNa8
Nc3xPa2 -4. b7-b8=R O-O -5. Bf1-g2 h4xg3 ep**.

Now, the 1st move of all 6 Rs is determined: wKR: **Rh1-g1**;
wQR: **O-O-O**; bKR: **O-O**; bQR: **
Ra8-b8**; wh. promoted R: **Rb8xNa8**; bl. promoted
R: **Rg1-h1**.