Anand and Bobby both are members of their school's chess club. And while cleaning up the games room at the end of the day, they saw a board with the following position:
[FEN "rbR1B1Q1/k1n1nN1p/p1pNpBb1/PpKPRqpP/1PP1PrP1/5p2/5P2/8 w - b6 0 1"]
Then the following conversation happened:
- Anand claimed that if it were white to move, white has a mate in 1
- Bobby then pointed out that if any non-king piece is removed from the board, there is no longer mate in 1
- Anand agreed, and further pointed out that in fact there is exactly one combination of two non-king pieces that he can remove from the original position that would still result in a mate in 1
Can you prove each of the statements above?
Source: myself, inspired by my answer to a puzzling question (spoilers in there for the first two questions)