## A Two-Player Board Game
*March 20, 2011*

*Posted by Saketh in : bonus , trackback*

On a 5×5 board, two players, Albert and Billy, alternately mark numbers on empty cells. The first player, Albert, always marks 1′s, the second, Billy, 0′s. One number is marked per turn, until the board is filled. For each of the nine 3 x 3 squares the sum of the nine numbers on its cells is computed. How large can the Albert force the maximum of these sums to be regardless of Billy’s behavior?

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