# Heart on a chessboard

talzamir
Posers and Puzzles 13 Dec '11 11:11
1. talzamir
Art, not a Toil
13 Dec '11 11:11
A king, a queen, a rook, a bishop, and a knight are on a chessboard on the edge of a heart shape, in some order, on squares C7, E7, B5, F5, and D3. They threaten the squares B6, F6, C4 and D4, but each of those four squares is threatened by exactly one piece. How many pieces threaten the center of the heart at D6?
2. 13 Dec '11 18:33
I count 2.
3. 29 Dec '11 20:58
Hmm. I'm not sure if I'm making a mistake or if the question is worded wrong, but it seems like 4 of them or 2 of them, depending on where you put the queen. I get 4 if the queen is on C7, E7 or D3, but only 2 if you put it on B5 or F5. What's gone wrong?
4. talzamir
Art, not a Toil
29 Dec '11 23:45
Always possible I've gotten something wrong.. such as, the heart goes through e4, not d4. The choices in the queen's position are limited by the requirement that each free square on the edge of the heart is controlled by exactly one officer. If there is alternative solution with the center controlled by four, great.
5. 02 Jan '12 04:28
With the pieces at
Kc7 Qe7 Bd5 Nf5 Rd3
, four of them control d6.