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 4x4 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 column, are marked with "X". What is the maximum possible number of times a player has to press the button to finish the game?

• A. 16
• B. 10
• C. 13
• D. 04
• E. 06

Hint:

When dealing with grid-based problems, consider the worst-case scenario where the conditions to finish the game are met as late as possible.

Answer 1

The Correct Option is C

Step 1: Understand the grid and conditions.
The grid is 4x4, and the game ends when all cells in any row or column are marked. Thus, it is possible for the game to finish early when one row or column is completely marked.
Step 2: Calculate the maximum number of moves.
The maximum number of moves occurs when no row or column is fully marked until the very last move. This gives a maximum of 13 moves before the game ends.
Final Answer: \[ \boxed{\text{(C) 13}} \]