Neurobics

Answers to Chess Problems

Russell Dear

(2a) 32 knights can be placed on a chessboard (on the black squares) without any two being able to attack each other. (2b) The smallest number of knights that can be placed so that all unoccupied squares are under attack is 12. As far as I know, there is only one solution to this problem.

(4) A five-by-five board with its centre square missing can be bisected into congruent halves in fifteen ways.

(5) The game is uninteresting in that if played intelligently white must win (mind you, that doesn't stop millions of people enjoying the game nought and crosses which always ends in a draw if played intelligently). According to David Silverman, one check chess can be made more interesting if the winner is the first to check with a piece that cannot be taken. In this case, as far as I know, either player can win when both sides play their best.

(6) My friend was being inscrutable again. What is a gudgeon?

Russell Dear is a Mathematician living in Invercargill