Question

In a computer game, each move requires pressing a button. When the button is pressed for the first time, as a move, the computer randomly chooses a cell from a $4	imes4$ grid of sixteen cells and puts an “X” mark on that cell. When the button is pressed subsequently, the computer randomly chooses a cell from the remaining unmarked cells and puts an “X” mark on that cell. This goes on till the end of the game. The game ends when either all the cells in any one row, or all the cells in any one co

Accepted Answer

D. To maximize the number of moves before completing a full row or column, we want to place as many 'X's as possible without filling any row or column completely. In a $4 	imes 4$ grid, if we mark 3 cells in each row and column, we can do so by leaving 1 cell unmarked in each row and column (e.g., the main diagonal of 4 cells). Leaving 4 cells unmarked allows $16 - 4 = 12$ marked cells without completing any row or column. The $13^{	ext{th}}$ press must mark one of the remaining 4 diagonal cells, which completes both a row and a column. Thus, the maximum number of presses required to finish the game is 13.

Maximum Button Presses in Grid Game

Explanation

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