Solutions

**4 - A. Baiburin**

1. Ne5? Ke6 2. Kf3 Kf5/Kd5 3. Nd4/Nc7#. But black has the move!

0. .. Kc6 1. Nbd6 Kd5/Kd7 2. N4c5 Kc6 3. Ne7#. The other variants are
similar, due to symmetry.

**5 - A. Yarosh**

The position is legal. Last moves were: **-1. Qh5-h2 Re8-g8 -2.
c4-c5 Re4-e8 -3. c3-c4 Ra4-e4 -4. a5-a6 Ra1-a4 -5. a4-a5 a2-a1=R -6.
c2-c3 b3xNa2! -7. Nb4-a2 c4xBb3 -8. Nc6-b4 c5-c4 -9. Nb8-c6 c6-c5 -10.
Na6xRb8! Ra8-b8** etc. Retracting -6. .. b3xBa2 or -6. b3xRa2
-7. Ra1-a2 c4xBb3 fails on retro-stalemate, because white can't get
his bishop fast enough to f1.

**6 - N. Burlyaev**

The position, after adding the pieces, and colouring them, is:

Retro-play is: **-1. Nd2-b1 h4-h3 -2. Nb1-a3 Ba3-b4 -3. Nf3-d2
Bb4-a3 -4. Qa3-b3 h5-h4 -5. Rb3-c3** and the position unlocks.

**7 - A. Zolotarev**

Retro-play is: **-1. ... f7xQe6 -2. Qd6-e6 Ne8-c7 -3. Qb8-d6 d4xBe3
-4. b7-b8=Q d5-d4 -5. b6-b7 d6-d5 -6. a5xBb6**. Further retroplay
includes: a4-a5; Bb8->e3; b4-b8=B; b5xRc4; c7xRd6; Rg8-c4; g4-g8=R;
Rg8-d6; g6-g8=R; Bf8->?; g7xf6. The minimum number of knight moves is
7 (Nb1-c3-e4, Ng1-e2, Ng8-f6-e8-c7, Nb8-c6).

**8 - A Zolotarev**

Retroplay is: **-1. ... b7xBc6 -2. Bd5-c6 d2xBc1=Q -3. Bg8-d5
e3xBd2 -4. g7-g8=B e4-e3 -5. h6xNg7**. Further retroplay includes:
Bf8->d2; f3-f8=B; Bf8->c1; f4-f8=B; f5xRe4; Ra8-e4; a6-a8=R; a7xNb6.
The minimum number of queen moves is 0!

**9 - A. Zolotarev**

Retro-play is: **-1. ... Qc1xNb2 -2. Nc4-b2 d2xBc1=Q -3. Ne5-c4
e3xNd2 -4. Nf7-e5 e4-e3 -5. Nh6-f7 e5-e4 -6. Ng8-h6 c7-c6 -7. g7-g8=N
c6-c5 -8. h6xRg7**. Further retro-play includes: Nf8-e6->d2;
f4-f8=N; Bf8->c1; f5-f8=B; e6-e5; f7xBe6 (this has to happen on a white
square!); Ba8->e6; a6-a8=B; a7xNb6 etc. The minimum number of queen
moves is 1: Qc1xb2.

**10 - B. Lure & A. Nazarov**

1. fg3(ep) OO 2. c1=R Re2#

**11 - B. Lure & A. Nazarov**

1. fg3 Nf2 2. f5 Be7#

1. bc6 f6 2. Bd6 Bf7#

**12 - A. Nazarov**

1. cd3 Kf4 2. e5 de6#

**13 - A. Shitov**

Retroplay is: **-1. ... Re1-e2 -2. Bg4-d1 Ke2-f1 -3. Bd7-g4 Kd1-e2
-4. B~ Qf1-g1 -5. B~ Qe2-f1 -6. B~ Qg4-e2 -7. B~ Ke2-d1 -8. B~ Rc1-e1
-9. B~ Rd1-h1 Bh4-g3 -10. Rh1-h2 Qg3-g4 -11. B~ Qh2-g3 -12. B~ Qg1-h2
-13. B~ Qe1-g1 -14. B~ Kf1-e2 -15. Rh2-h1 Kg1-f1 -16. B~ Nc7-a8 -17.
B~ Nd5-c7 -18. B~ Nf6-d5 -19. B~ Ne4-f6 -20. B~ Ng3-e4 -21. B~ Nf1-g3
-22. B~ Qe2-e1 -23. Re1-d1 Qh5-e2 -24. Re2-e1 Ng3-f1 -25. B~ Rf1-c1
-26. Re1-e2 Q~ -27. Rc1-e1 Rd1-f1 -28. B~ Kf1-g1 -29. B~ Ke2-f1 -30.
Rh1-h2 Q~ -31. h2-h3!**. So at least 59 moves past without
a capture or a pawn move.

**14 - N. Burlyaev**

The position, after colouring, is:

Black has no last move. The last moves were: **-1. Qb3-b4 Ka5-b6
-2. Rb4-a4 Kb6-a5**, so mate in 1 with 1. ... e6#

**15 - A. Kislyak**

The position is legal. Last moves were: **-1. Qb1xQb2 Qa2-b2 -2.
Bb2-a3 Qa8-a2 -3. h6-h7 Qe8-a8 -4. h5-h6 Qg6-e8 -5. h4-h5 Qg1-g6 -6.
h3-h4 g2-g1=Q -7. h2-h3 h3xQg2 -8. Qg6-g2 h4-h3 -9. Qe8-g6 h5-h4 -10.
Qa8-e8 h6-h5 -11. a7-a8=Q h7-h6 -12. a6-a7 a7xNb6 -13. Ka5-b5 Kc4-b3**
and everything unlocks.

**16 - V. Peretyatko**

Black has the pawn from a4 in his hand, and is playing ab3 ep. Proof
game is:

1. c3 a5 2. Qc2 a4 3. Qh7 Ra5 4. Qg7 Rh3 5. Qg4 Rg5 6. d3 e5 7. Be3
Ke7 8. Nd2 Kd6 9. OOO Kc6 10. Kc2 Kb5 11. Qc4 Ka5 12. f4 Rf3 13. h4
Rf1 14. Ngf3 Rf2 15. Rhf1 Ne7 16. b4 **ab3**

**17 - A. Yarosh**

Retract **-1. Bh2-g1 Kd8-e8 -2. Bd6-h2 Kc8-d8 -3. Bc5-d6**
(if white retracted Bd4-e5-h2, black can now retract Kb8-c8!, forcing
white to retract Nc5-a6) **Rd8-f8 -4. Ng6xQh8!** (-4. Ba7-c5?
OOO!) and now black can't retract queenside castling, because the queen
would be trapped in the h8-corner. Finish now with **-5. Ba7-c5
-6. Bb8-a7 -7. a7xBb8=B**, and play forward 1. a7xb8=Q/R#

However, this is cooked: **-4. Ba7-c5! OOO -5. Ng6-h8 Rf8-g8 -6.
Nf4-g6 Rg8-f8 -7. Ne6-f4** and play forward **1. Na6xc7#**.
Black can't uncapture anything on his 5th move: The only piece which
could've reached g8 is a knight, and this requires too many captures:
a7xb8=N, and cxbxaxb8=B. The bishops were captured on their home squares.
Because black retracted castling, the king and rook are immovable.

**18 - A. Zolotarev**

The position is legal. The whole cage unlocks by retracting d7xc6. Retro-play
is: **-1. ... Rb6xQa6 -2. h4-h5 e6xNd5 -3. Ne3-d5 Ne1-c2 -4. Nc2-e3
Nd3-e1 -5. h2-h4! Nc5-d3 -6. Qb5-a6 Na6-c5 -7. Qh5-b5 g5-g4 -8. Qh3-h5
e7-e6 -9. Qc8xPh3 h4-h3 -10. Qg8-c8 h5-h4 -11. g7-g8=Q h6-h5 -12. g6-g7
h7-h6 -13. f5xBg6 Bh5-g6 -14. f4-f5 Bg4-h5 -15. f3-f4 Bc8-g4 -16. f2-f3
d7xRc6** and the whole position unlocks.

**28 - N. Zinoviev**

**(a)** 1. Qh8#?. But black has the move: 0. .. b6/b5 1.
Qa6#

**(b)** 1. Qa1#?. But black has the move: 0. .. b6/b5 1.
Qh1#

**29 - V. Voinov**

Retract -1. c2-c4, and #3 with 1. c4! bc3 2. Nb6 c2 3. Nc4#

**30 - V. Zhupikov**

1. Bc6? / 1. Re7?. But black has the move!

0. .. Nf5 1. Kc7 Nd6 2. Bb7 Ka7 3. Ra8# 1. .. Ka7 2. Bb7 ~ 3. Ra8#

0. .. Nc8 1. Kc7 Ka7 2. Ba7 c5/cd5/d6/de6/Nb6/Nd6/Ne7 3. Ra6/Ra6/Nc6/Nc6/ab6/Ra8/Ra8#
1. .. de6/Nd6 2. Bb7 Ka7 3. Nc6/Ra8#

**31 - V. Peretyatko**

1. Bc4#? But black's last move could've only been e4xf3. But the only
missing white piece is the black-squared bishop (Bh8 is clearly promoted).
So black has the move.

0. .. Rb5/Bb5/Kb5/a3 1. Nc4/Nd5/Qb1/Bc4#

**32 - M. Kormilshev**

Add a black rook on a1. All black captures were done by the two pawns
on h2 and h3, so black has no possible last move. 1. ... Rc1! and black
doesn't lose.

**33 + 34 - G. Kukin**

Upper left corner (depicts a 'C'): 1. c6! Rc6/Rb8/~ 2. Bc6/ab8=Q/Sc7#

Upper right corner (depicts a Russian 'L'): 1. Rf8 (2. Nf7/Rg8) Rh6
2. Rh6#

Lower left corner (depicts an 'A') : 1. Nd1 Nc4 2. Bc3 Bb1#

Lower right corner (depicts a Russian 'G'): 1. Kh1 Kh3 2. g2 Nf2#

**35 - W. Churtornoi**

1. g8=B? Ke8! 1. g8=R? Ke6! 1. g8=K! Ke6/Ke8 2. Bc8/Bc6#

**36 - B. Formanek**

Retract -1. d7-d8=K! and play forward 1. d7xc8=K! =

**37 - L. Grolman**

1. Be3 Rb4 2. Be4 Bb3! and now you see 1-0 on the board!

**44 - A. Shitov**

1. Bc4#! Last moves could have been: -1. ... Kd6-e6 -2. e7xd8=R / -1.
... Kd7-e6 -2. c7xd8=R / -1. ... Kf6-e6 -2. g7xf8=Q / -1. ... Kf7-e6
-2. e7xf8=Q

**45 - A. Stepanov**

White's pawns captured 14 times. Suppose white has the move. Now there
are three possible last black moves:

-1. .. Bg7-f8 -2. Ng8-f6 Bf8-g7 -3. Nf6-g8 ... and we're stuck in a
neverending cycle.

-1. .. Bg7xQf8 -2. Ng8-f6 and retrostalemate

-2. .. Bf8xQg7 illegal check

So black has the move. Stalemate, so the game is draw!

**46 - K. Tina**

It's possible to reach the position with only one queen-move: Qd8-d5.

Last moves were: **-1. Nc2-e3 e5xNd4 -2. Ne6-d4 c3xNd2 -3. Nf8-e6
e6-e5 -4. f7-f8=N d4xNc3 g6xNf7**. Now white unpromotes both
uncaptured knights on f8. Black uncaptures f7xRe6, white retracts this
rook to a8, unpromotes the pawn, and retracts it to a6. Finally black
uncaptures a7xNb6, and the whole position unlocks.

**47 - A. Zolotarev**

Last moves were: **-1. .. Ba3xRb4 -2. Rd4-b4 Rb4-b3 -3. Rd6-d4 f4xSe3
-4. Re6-d6 f5-f4 -5. Re8-e6 f6-f5 -6. e7-e8=R g4-g3 -7. e6-e7 g5-g4
-8. d5xBe6** and further: (Bg8-e6); (Bh7xSg8); Sd3-e3; Rh1-e2; (Bh3-h7);
Sh8-d3; g6-g8=S; h5-h8=S; (g7xQf6); (h6xQg5); Qb8-f6; b5-b8=Q; Qb8-g5;
(Ba6-h3); b7-b8=Q; (h7-h6); b6-b7; (Bc8-a6); (b7xBc6).

So the shortest route for a knight is 0 moves!

**48 - V. Peretyatko**

The coloured position is:

Last moves were: **-1. Qh8(g7/f6)-e5 e5-e4**.

**49 - B. Gusev**

The last moves were: **-1. Sc3-b1 Rh5-h7 -2. Bc1-b2 Rh4-h5 -3. b2-b3
Rh3-h4 -4. Rb3-b4 Rh2-h3 -5. Ra3-b3 Rh1-h2 -6. Ra2-a3 h2-h1=R -7. a3-a4
h3-h2 -8. Ba4-b5 h4-h3 -9. Bd1-a4 h5-h4 -10. Be2-d1 h6-h5 -11. Bf1-e2
h7-h6 -12. e2xBd3**.

So the shortest route for the rook is Rh1-h2-h3-h4-h5-h7.

**62 - A. Yarosh**

Black has no legal last move, so he has the move. Mate in 2 with 0.
.. Rc8 1. R8e7 Kd8 2. Rcd6#/0. .. Re8 1. R8c7 Kd8 2. Red6#

**63 - A. Yarosh**

The king on f1 is white, the other pieces are black. Black retracts
c2xQb1=N, and h#1 with 1. c1=B Qb3#

**64 - V. Baikin**

The position is illegal. For a correction, see
here.

**65 - V. Peretyatko**

White has three promoted pieces. One is the g-pawn, which promoted after
g6xh7-h8=R, one is the c-pawn which promoted after c5xBd6-d8=R, and
the last is the a-pawn which promoted on a8 to a bishop. The black a-pawn
was captured on its own file.

Because white captured the bishop on d6, black can't retract d6-d5 too
soon. Because the white bishop had to leave a8, black can't retract
b7-b6 too soon. Because the bishop from f8 was captured on d6, black
can't retract e7-e6 too soon. So until something is uncaptured, black
only has king-moves. The last moves must've been **-1. Nf3-e1
Kf1-e2 -2. Rg2-g1 Ke2-f1 -3. Nf2-d1 Kf1-e2 -4. Ne1-f3 Ke2-f1 -5. Rf3-f4
Kf1-e2**, and the whole position can get released.

So the mate is legal.

**66 - A. Kornilov & A. Frolkin**

The position unlocks after black can retract h6-h5, and white can uncapture
h5xg6. For this, a black piece is needed on g8. A white knight can uncapture
this piece on g7. So black needs to uncapture a white knight. The white
captures are also g2xf3, h5xg6, dxexf and Nxg7. So the black a-pawn
promoted on b1, after capturing once on the b-line. So the black captures
are axb, bxc, cxd and exd. So black must uncapture a knight with his
a-pawn, after which this pawn promotes. So black must unpromote Ng1
on b1.

The last moves were: **-1. g6-g7 h4-h3 -2. a6-a7 Nh3-g1 -3. a5-a6
Nf4-h3 -4. a4-a5 Nd3-f4 -5. a3-a4 Nb4-d3 -6. a2-a3 Nc2-b4 -7. b6-b7
Na3-c2 -8. b5-b6 Nb1-a3 -9. b4-b5 b2-b1=N -10. b3-b4 a3xNb2 -11. Nd3-b2
a4-a3 -12. Nf4-d3 a5-a4 -13. Nh5-f4 a6-a5 -14. Ng7-h5 a7-a6 -15. Ne8xRg7
Rg8-g7 -16. Qh8-h7 h5-h4 -17. Kh7-h6 h6-h5 -18. h5xNg6** and
the whole position unlocks.

But this is **cooked**: Retroplay could be too: b4-b7; (b7xBc6);
c2-c7; (c7xBd6); (d6-d5); a4xSb3-b1=B-e6.

**67 - A. Kornilov & A. Frolkin**

Retroplay is: c2xSd3; Sb4xRd3!; Re8-d3; Ra8xQe8; (Qb8xSe8); Sg7-e8;
Se8xRg7; (Rh7-g7); Qh8-g8; Kg8-f8; Rf8-a8; (Ra1-e7); (b3xPa2-a1=R) etc.

**68 - A. Zolotarev**

Retroplay is: **-1. .. Ba3xRb4 -2. Rd4-b4 Rb4-a4 -3. Rd6-d4 f5-f4 -4.
Re6-d6 f6-f5 -5. Re8-e6 f4xBe3 -6. e7-e8=R g5xQf4 -7. e6-e7 g6-g5 -8.
d5xBe6** and further: Bh8-e3; h2-h8=B; (h7xQg6); __Qg8-g6__; (g7xQf6);
Bd3-f1; Rh1-e2; Bf1-d3; Qb8-f4; b6-b8=Q; Qb8-f6; (Bb7-e6); b5-b6; (Ba6-b7);
b7-b8=Q; (__Qd8-c8__); b6-b7; (Bc8-a6); (b7xRc6).

So the shortest white queen-move is Qg8-g6, and the shortest black queen-move
is Qd8-c8.

**82 - V. Peretyatko**

Black still has 8 pawns, so Bg1 is the original bishop from f8. So the
move-order is: g7-g6; Bf8-g1; Bc1-h2; g2-g3. So g6 was already there
when g2-g3 was played. So Bh7 is a promoted white pawn. It must be the
white b-pawn, which played b2xc3xd4xe5xf6xg7-g8=B. Together with the
bishop on c8, these are all the missing black pieces. So white's last
move wasn't a capture. The only way the position can be explained is
if the last moves were **-1. Nc1-d3 Ka1xNb1 -2. Nc3-b1 Kb1-a1
-3. Nd5-c3 Ka1-b1 -4. Nf6-d5**. The white bishop on f1 was captured
on its homesquare, and on b6, black captured the missing rook. So the
position is indeed legal.

**83 - A. Kornilov**

Retroplay is: **-1. .. Rc2-c1# -2. Kb1xNa1 Nb3-a1 -3. Ka1-b1 Na5-b3
-4. Kb1-a1 Nc4-a5 -5. Ka1-b1 Na3-c4 -6. h3-h4 Nb1-a3 -7. h2-h3 Rc1-c2
-8. c2-c3 c3xB/Nd2** and further retroplay involves bRc1 -> a8;
a7xNb6; wKa1 -> f8; Re8-e7 and the whole thing opens up.

This problem was published in feenschach too.

**84 - A. Yarosh**

The intention was:

But this is **cooked**:

**85 - V. Liskovets**

Suppose white may still castle. The white pawns captured seven times:
b2xa3, c2xb3xa4, dxcxbxa7, and fxg. None of these captures were on the
d-line, so either the black d-pawn promoted, or it's one of the pawns
on the g- or h-file. In the first case, because white may still castle,
black had to capture dxc before the promotion. So the black captures
are gxh, fxgxh, dxc, and exfxg. None of these captures is on the e-file,
so the e-pawn had to promote to get captured. So black may not castle
in this case. In the other case, black captured six times with the pawns
currently on the g- and h-file. This would imply the black e-pawn promoted
without capture, which isn't possible, since white may still castle.

So castlings are mutually exclusive.

h#2 with 1. Rd8 OO 2. Rf8 Re1# or 1. hg4 Ke2 (OO?) 2. OOO Rc1#.

**86 - V. Slobodenyuk**

**(a)**: Black only misses the white-squared bishop. So
the last move wasn't b6xc7, d6xc7 or g3xf4. So the last move must've
been f2-f4. h#3 with 1. ef3 ep c8=R 2. Nd5 e4 3. Rf4 Rg8#

**(b)**: Now the last move could've been b6xQc7. h#3 with
1. Kf5 c8=N 2. Ng4 e3 3. Be6 Ne7#

**87 - V. Soloviev**

g2-g3 was played after Bg3-h2, and b2-b3 was played after B-a2. So one
of the bishops b1 or h2 is promoted, and the original bishop was captured.
Black's only capture was g7xf6, so the bishop on h2 is a promoted one.
So a2 promoted on a black square, and he needs three captures for that.
Together with h2xg3xf4 that's all missing black pieces.

First bring the white king to e1, the white queen to d1, the white bishop
to a2, the white rook to b5, and the white knights to b1 and g1. Then,
after taking the black bishop back to f8, uncapture g7xf6. If black
may still castle in the diagram position, he now only has waiting moves
with his pawns. The fastest way to a white uncapture is: **-1.
.. g7xf6 -2. Bb2-f6 c5-c4 -3. Bc1-b2 d6-d5 -4. b2-b3 c6-c5 -5. Bd5-a2
c7-c6 -6. Bg2-d5 h5-h4 -7. Bf1-g2 h6-h5 -8. g2-g3 h7-h6 -9. Bg3-h2 a6-a5
-10. Bh4-g3?? -11. g3xf4.**. If black may still castle, he has
no move on the question marks.

So black may no longer castle. Mate in 3 with 1. Qb4 (2. Qe7) c3 2.
dc3 (3. Qe7) ab4/Kf8 3. Ra8/Rc8#, or 1. Qa5 c3 2. Qc3 ~ 3. Ra8#.

**101 - V. Voinov**

Retract c7xBb8=N, and mate in 2 with 1. c8=Q ~ 2. Qb7#

**102 - V. Voinov**

Retract h5xg6 ep!, and mate in 2 with 1. Kd6 g4 2. Qe5#

**103 - V. Voinov**

Retract Rf4-f1, and mate in 2 with 1. OO Kh3 2. R1f3#

**104 - A. Kislyak**

White captures are gxPh, axNb, and Bc8 on his homesquare. Black captures
are c7xb6xa5 and the f-pawn on its own file. The position unlocks when
black uncaptures b6xNa5. For this, the white king must leave the 8th
rank.

Last moves were: **-1. Kb8-c8 Kd8-e8**. Now the black king
makes waitingmoves between d8 and e8, while the white knights go to
c8 and h8. The white pawn on h7 goes to h2, the knight on h8 unpromotes
and then the retroplay is: **Kd8-e8 g3xPh4 Ke8-d8 Kc7-b8 h5-h4
Kb6-c7**. Now black can uncapture b6xNa5, and the whole position
unlocks.

**105 - Y. Lebedev**

The last moves were: **-1. .. f7xNe6 -2. Nd8-e6 e5xNf4 -3. d7-d8=N
d6xRe5 -4. c6xQd7 Qd8-d7**. White now unpromotes the uncaptured
knight from f4 on a8, and retracts this pawn to a2. Black uncaptures
a3xRb2. Both uncaptured rooks from b2 and e5 unpromote on g8, black
brings back his bishop to f8, and uncaptures g7xPf6, and the whole position
unlocks.

So the game could've started with 1. c2-c3.

**106 - V. Peretyatko**

Visual black captures are fxe, cxdxexfxg2, and b3xc2. Black needs to
uncapture a white piece with his last move, or white is retropat. This
accounts for all missing white pieces. So white can't retract c2-c3
until one of the queens is unpromoted, and he can't retract d2-d3 until
Bc1 (and Ra1) are back on their homesquare again.

The last moves were: **-1. .. Rg7xNh7 -2. Nf8-h7 Be8-f7 -3. f7-f8=N
Qe5-f6 -4. f6-f7 Rf4-f5 -5. f5-f6 Kf6-g5 -6. h4-h5** and the
position unlocks.

So the mate is legal.

**107 - V. Liskovets**

**1. Ra8 2. OOO 3. Rd2 4. Rh2 5. Rd2 6. h2 7. h1=B 8. Bc6 9. Kb7
10. Ka6 11. Kb5 12. Ka4 13. Bb5** Now white's last move must've
been b2-b4. **14. cb3 ab3#**

But this is cooked: 1. Sc6 2. Ra8 3. OOO 4. Kb7 5. Ka6 6. Kb5 7. Ka4
8. Rd2 9. cb3 10. Rd4 11. Rb4 12. Rb5 13. Sb4 ab3#.

**108 - A. Zolotarev**

The position unlocks when white can retract d2xPe3 and g2-g3. One of
the black knights is the promoted a-pawn, it promoted on either a1 or
c1 after two captures. Together with gxf, these account for all missing
white pieces. White captured hxBg and d2xPe3.

The position unlocks after **-1. .. Nc6-b8 -2. Nd5-e7 Ne7-c6 -3.
Nc3-d5 f5-f4 -4. Ne4-c3 Ne6-g5 -5. Ng5-e4 Nc5-e6 -6. a7-a8=B Nb3-c5
-7. a6-a7 Nc1-b3 -8. a5-a6 c2-c1=N -9. a4-a5 b3xBc2 -10. Be4-c2 b4-b3
-11. Bc6-e4 a5xBb4 -12. Bd2-b4 a6-a5 -13. Bc1-d2 a7-a6 -14. d2xPe3 e4-e3
-15. Ra3-f3 e5-e4 -16. Bg2-c6 e6-e5 -17. Bf1-g2 Kf4-g4 -18. g2-g3**
and the whole position unlocks.

So white has the move. Mate in 1 with 1. Rf4#! and not with 1. .. Nd7#?

**117 - V. Zhupikov**

1. b3? a4 2. b4 a3 3. Kc6 a2 4. Bb7#, but black has the move: 0. ..
a4 1. Be4! a3 [1. .. Ka5 2. Bd3 a3 [2. .. a6 3. Bc2 a3 4. b5#] 3. b4
Ka4 4. Bc2#] 2. b4 a2 3. Kc6 a1=Q 4. Bd3#

**118 - V. Voinov**

Retract -1. .. Ng4xPh6, and #4 with 1. .. Ne5 2. Kh7 Nd7 3. Nh8 Nf8
4. h7 Ng6#

**119 - V. Voinov**

**(a)**: Retract -1. Kb3xNb4, and play forward 1. Na3 N~ 2. Nc2#

**(b)**: Retract -1. Kb3xPb4, and play forward 1. Na3 ba3 2. Kc2
a2 3. Nb3#

**120 - A. Oleinik**

Black has no last move. #3 with 0. .. h5 [0. .. h6? 1. g6 h5 2. Bf6#]
1. g4 Kh7 [1. .. hg4 2. g6 g3 3. Bf6#] 2. g6 Kh6 [2. .. Kh8 3. Bg6#]
3. g5#

**121 - A. Shitov**

Retroplay is: **-1. Rd6-d3 a4-a3 -2. Bc5-g1 a5-a4 -3. Ba3-c5 a6-a5
-4. Bc1-a3 a7-a6 -5. Rd4-d6 g3-g2 -6. Rb4-d4 g4-g3 -7. Rb1-b4 h5xQg4
-8. b2xc3**. So black has the move. Not 1. f8=Q? or 1. Ng6?, but 1.
.. Rg7#

**122 - M. Shalikovski**

Retroplay is: **-1. Bg4-h5 Bf1-h3 -2. Bh3-g4 Bg2-f1 -3. Bg1-h2 Bf1-g2
-4. Bg2-h3 h2-h1=N -5. Bh1-g2 Bh3-f1 -6. Bg2-f1 Bg4-h3 -7. Bf1-g2
Bh3-g4 -8. g2-g3** etc.

**123 - A. Zolotarev**

Retroplay is: **-1. .. Ra1-a2 -2. e2xNf3 Nd2-f3 -3. g3-g4 Nb3-d2 -4.
Ba2-b1 Rh1-a1 -5. Bb1-a2 h2-h1=R -6. Ba2-b1 h3-h2 -7. Bb1-a2 h4-h3 -8.
Ba2-b1 h5-h4 -9. Bb1-a2 h7-h5 -10. h6xQg7 Qd4-g7 -11. Ba2-b1 Qd1-d4
-12. Bb1-a2 Qc1-d1 -13. Ba2-b1 Qa1-c1 -14. Bb1-a2 Qa2-a1 -15. h5-h6
Nd2-b3 -16. h4-h5 Qb3-a2 -17. Ba2-b1 Ne4-d2 -18. Bb1-a2 Nf6-d4 -19.
Rd1-d7 Nd7-f6 -20. Ba2-b1 e7-e6 -21. Ra1-d1 d6xBc5 -22. Bb1-a2 Qa2-b3
-23. Be3-c5 Qb3-a2 -24. Bc1-e3 Qa2-b3 -25. d2xRc3** and the position
unlocks.

**124 - A. Kislyak**

Add a black queen on a1, and retroplay is: **-1. Rd3-d8 h4-h3 -2. Rf3-d3
h5-h4 -3. Rf6xPf3 f4-f3 -4. Rh6-f6 f5-f4 -5. Rh8-h6 f6-f5 -6. h7-h8=R
f7-f6 -7. g6xRh7 Rh6-h7 -8. g5-g6 Rd6-h6 -9. g4-g5 Rd8-d6 -10. g3-g4
d7xRc6** and the position unlocks.

But this is **cooked**: Add a black queen or knight on a1, and last
move was d7xRc6. The rook on d8 promoted after f7xRe8=R.

**125 - A. Kornilov**

If black moved last, his last move must've been Kh1-h2, but this leads
to a retro-repetition of moves. So black has the move. #1 with 1. ..
fg1=Q#.

**126 - A. Kornilov**

Last moves were: **-1. a7xNb8=N Nc6xNb8**.

But this is **cooked**: -1. a7xNb8=N Nc6-b8 -2. Rf8xc8.

**F. Garde**

The coloured position is:

The last 19 moves were: **-1. .. Qd8xRe8 -2. a6-a7 h4-h3 -3. a5-a6
h5-h4 -4. a4-a5 h6-h5 -5. a2-a4 a3xBb2 -6. g4-g5 a4-a3 -7. Ng5-h7 a5-a4
-8. Bh7-g8 a6-a5 -9. Kg8-f8 a7-a6 -10. Rf8-e8 Qe8-d8** etc.

**133 - A. Oleinik**

Black has no last move. #4 with 0. .. bc6 1. c3 d5/d6 2. cd6 c5 3. d7
c4 4. d8=R/Q#

**135 - N. Veselov**

Retroplay is: **-1. .. Rg8-h8# -2. Bh5-g6 Rg6-g8** and further: (Rh1-g6);
Bf1-h5; Bb8-h2. Black captures were: c7xd6; e7xf6; g3xRh2. White captures
were: axbxcxRb8=B.

**136 - A. Kislyak**

Retroplay is: **-1. f7xRg8# Rf8-g8 -2. Nd3-f4 Rg8-f8 -3. Kh8-h7 Rg7-g8
-4. Kg8-h8 Rh7-g7 -5. Bf8-h6 Rh1-h7** and further: a2-a8=N-d3; (b2-b1=R-h1);
**-n. .. a3xRb2 -(n+1). Rh2-b2 a4-a3 -(n+2). Rh8-h1 a5-a4 -(n+3). h7-h8=R
a6-a5 -(n+4). h6-h7 a7-a6 -(n+5). h5-h6 h6xg5** and the position unlocks.

White captures: cxd, dxe, exdxe. Black captures: h6xg5, gxf and fxe.

**137 - A. Yarosh**

Retroplay: **-1. Rb3xNb2 Na4-b2 -2. Nb2-d1 Nc5-a4 -3. h7-h8=B Ne6-c5
-4. h6-h7 Ng5-e6 -5. h5-h6 Nh3-g5 -6. h4-h5 Ng1-h3 -7. h3-h4 g2-g1=N
-8. h2-h3 h3xNg2 -9. Nf4-g2 f6-f5 -10. Ne6-f4 f7-f6 -11. Nc7-e6 h4-h3
-12. Na8-c7 h5-h4 -13. a7-a8=N h6-h5 -14. a6-a7 h7-h6 -15. a5-a6 b7-b6
-16. a4-a5 a5xBb4** and the position unlocks.

**138 - A. Zolotarev**

Retroplay is: **-1. c2xRd3 Rg3-d3 -2. d7xBc8=Q Rg1-g3 -3. e6xBd7 g2-g1=R
-4. e5-e6 g3-g2 -5. e4-e5 h4xBg3 -6. e3-e4**. Further retractions
are: (h6-h4); (f7-f1=B-d7); (f4-f1=B-c8); f2xRe3; (b3-b1=R-e3); e3xRd4;
(b2-b1=R-d4); Ba3-g3; (b4-b3); __Qd1-g4__ (b2-b3); Bc1-a3; b2xRc3;
e2-e3 and the position unlocks. The extra white bishop is the g-pawn
which promoted on g8.

So the minimal number of queen moves is 2 (Qd1-g4 and Qd8-d6).