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If you exclude the squares a1 and h8, can you cover the board with 31 dominos?
Solution: No. A domino will always cover one white and one black square. As a1 and h8 are black, we are trying to cover 32 white and 30 black squares with dominos. This is impossible.
On an empty chessboard there is a rook on a1. It can only move one square at a time. Can it move onto every square on the board just once and end on the squares 1) a8 and on 2) h8?
Solution: The answer to part 1 is yes. A potential sequence of rook moves is a1-b1-c1-...-h1-h2-g2 -...- a2-a3-b3-...-h3-h4-...-a4-a5-...-h5-h6-...-a6-a7-...-h7-h8-...-a8.
The second part cannot be done because we need to make 63 moves to cover the whole board. After an odd number of moves the rook moves onto a white square. As h8 isn't white we cannot finish on it. The rook can easily reach the target square a8, which is white.
What is the greatest number of different mates in one move that can be delivered in a position with only the two kings and two white queens on the board?
Here is the position we were looking for:
White to play has 15 different ways to mate Black in one move. Note that the position with wQd6 instead of wQd5 is not correct, since Black could not have made the last move, and it must be Black to move. The diagram above could have arisen from wKg7, Qc1, d5; bKe7, after which 1.Qc7+ Ke8 was played – and it is White to play.
There are seven mirrored positions that also work.
Solutions
Solutions
Pollmächer: White has 47 moves that deliver mate – count them if you don't believe it.
Fabel: There is only one place on the board for the black king where White can mate in one. It cannot be on c1 because then the white king must have moved to let it in, and so castling is illegal and there is no mate in one. So the black king must be placed on f3 and the mating move is 1.0-0.
Vilhelm Roepke, Skakbladet, 1942
White to play and win
This is the easiest chess study ever composed: 1.d4 b5 2.d5 b4 3.axb4 a3 4.b5 a2 5.b6 a1=Q 6. b7 mate. Every move by both sides (except the irrelevant black promotion) is the only legal move in the position.
Fabel: White to play and win – how many moves?
Are there any chess engines out there that will announce mate in the initial position?
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