Chessboard Madness

You have unlimited number of knights, bishops, rooks and kings. What is the biggest number of pieces (any combination) you can place on a chessboard, so that no piece is attacked by another one?

If we put 32 knights on all black squares, then no two pieces will attack each other. Now let’s see that if we have more than 32 pieces, then there will be two which attack each other. Split the chessboard in 8 rectangular sectors of size 2×4. It is not hard to see that if we have more than 4 pieces in the same 2×4 sector, then 2 of them will attack each other. Therefore we can place at most 4 × 8 = 32 pieces on the chessboard.

Pinned Men

The following game is played under very specific rules – no pinned piece checks the opposite king. How can White mate Black in 2 moves?

First, White plays f3 and threatens mate with Qxe2. Indeed, blocking with the black rook on d4 will not help, because it will become pinned, which means that the rook on d6 will become unpinned, which will make the bishop on b6 pinned, and that will unpin the knight on c7, resulting in a mate. Below are listed all variations of the game.

1. … Rd5 2. Qxe2#
2. … Bxa5 2. Kc8#
3. … Bxc7 2. Nxc7#
4. … Bxe8 2. Kxe8#
5. … Qxe7+ 2. Kxe7#
6. … Rd2 2. Bxd2#
7. … Rxd6+ 2. Qxd6#

Mini Chess

White to play and force the black king to d3.

1. Qc3+ Ka2 2. Qc1 Kb3 3. Qa1 Kc2 4. Qa2+ Kc3 5. Qb1 Kd2 6. Qb2+ Kd1 7. Qa2 Kc1 8. Qb3 Kd2 9. Qb1 Kc3 10. Qa2 Kd3

If 4. … Kc1, then 5. Qb3 and we get to the position in move 8. If 4. … Kd1, then 5. Qb1 Kd2 6. Qb2+ and we get to the position in move 6.