MathDB

Two people play a game on a

9 \times 9

board. They move alternately. On each move, the first player draws a cross in an empty cell, and the second player draws a nought in an empty cell. When all

81

cells are filled, the number

K

of rows and columns in which there are more crosses and the number

H

of rows and columns in which there are more noughts are counted. The score for the first player is the difference

B = K- H

. Find a value of

B

such that the first player can guarantee a score of at least

B

, while the second player can hold the first player's score to at most B, regardless how the opponent plays.
(A Kanel)

Problem Statement