The crossword solution for the term 'Problem for a King' is MATE, which is a four-letter word. MATE is a chess term used to describe a situation in which a player's king is in check and cannot move out of check. This means that the king is in danger of being captured by the opponent's pieces. In this situation, the player must find a way to either capture the attacking piece or block its path. If neither of these options is available, then the game is lost and the player has been mated.