Puzzle 1

Raymond Smullyan
Manchester Guardian, 1957

Solution: If we try to put the wK in b3, it will be in check from bRb5 and bBd5 in an impossible way. But if we put him elsewhere, the bK will be in check from wBa4. Said check can only be explained if the wK just left square b3 and we are back to the original dilemma.

Well, not exactly the same dilemma. If the wK just left b3, he could have done so by capturing a black piece that could explain the impossible check !

Three moves ago, the position was:

Here the check is perfectly explainable. Play went on with 1. c2-c4 b4xc3ep+!! 2. Kb3xc3+. This is one more example of dirty tricks with en passant captures. In a very economical setting.

Finally, the White King must be on c3.

Puzzle 2

J.-L. Turco
diagrammes 60, 01/1983

Analysis: Queens did not move and have been captured at home (by enemy Knights). Kings and Rooks only performed oscillations. All in all we can check that White played an odd number of move while Black played an even number of moves. Thus White did move last and Black is to move.

Mate in 1: 1 ... Na1xc2 # and not the illegal 1. Nxf7??.

Puzzle 3

16 - W. Keym
Die Schwalbe, 1971
1st/2nd Prize Ceriani Mem. Tourney

There are 8 possible en-passant captures half-finished.

• e5xd6 ep: This requires as last black move d7-d5. But because the white pawns captured 3 times, the bishop can't have captured on e6, so the check is illegal.
• c5xd6 ep: Same reasoning.
• c5xb6 ep: The white pawns captured 3 times before this move. The black pawns on d5 and e3 captured twice. So the missing pawns, which were captured by the white pawns, didn't capture, so they couldn't have promoted. But none of these pawns could've reached the b- or g-line. So this ep-capture is illegal too.
• a5xb6 ep: The pawns on the a- and b-line, and the pawns on the d- and e-line cross-captured, once by black and once by white. Together with the capture on the g-line this accounts for all captures. But then, like in the previous case, the missing black pawns couldn't have reached squares where they could get captured.
• d4xe3 ep: White captured twice, on b6 and on the g-line. So the d-pawn didn't capture, which means that the two black pawns on the d-line come from the c- and e-pawn. But then the d-pawn and the f-pawn were captured on their own line, so neither of them reached the b- or g-line.
• f4xe3 ep: Black captures are [c/e]xd5 and Bxd3. Both captures were on white squares, and white misses the black-squared bishop.
• h4xg3 ep White captures are, again, a5xb6 and hxg. The black pawns on the d- and e-line captured twice, so the missing two pawns couldn't have promoted and got captured on their own line.
• f4xg3 ep This is the only legal option. The missing h-pawn promoted on h1, after hxg was played. The other pawn got captured on its own line. A possible move-sequence could be for instance: a5xRb6; a7-..-a3; h6xQg7; h7-..-h1=Q; e2-e4; d4xBe3; d2-..-d6; c6xRd5;

So the only legal en-passant capture was f4xg3. So Black mates in ½ by removing the white pawn on g4.