A king is placed at the left lower corner of the 8 8 checker

A king is placed at the left lower corner of the 8 ×8 checkerboard. Two players take turns moving the king one square to the right, or upward, or diagonally right and upward. Whoever cannot make a move loses. Determine who has a winning strategy and describe the strategy.

Solution

Solution:

The second player wins. The strategy is to always return the King to the main
diagonal.

As we can visualize that second has always chance to return it main position, because whenever the first player play or tunrs his move the second one can move back to (8,8) position ( left lower corner). But if player second moves any posistion like (8,6) ( lower right from (8,7) position to just one right ) , at this moment B can\'t take it back to the main diagonal that means player A is unable to take move.