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: Grid and Termination Conditions.
The grid is 4x4. The game concludes when any single row or column is entirely marked. Consequently, the game can terminate prematurely if a row or column is completed before all cells are marked.

Step 2: Maximum Moves Calculation.
The maximum number of moves is achieved when no row or column becomes fully marked until the final move. This scenario allows for a maximum of 13 moves prior to the game's conclusion.

Final Answer:
\[
\boxed{\text{(C) 13}}\]