There are 9 balls. Two students, A and B, take turns to draw balls without replacement. Each time, they can draw at least 1 ball and at most 3 balls. The player who draws the last ball wins. If A draws first, which of the following statements is correct?
Pick one
Solution
To solve this problem, we analyze the situation step by step, following the strategy provided in the solution:
1. Initial Move by A: A starts the game by drawing 1 ball. This leaves 8 balls remaining.
2. Response Strategy:
- If B draws 1 ball, 7 balls remain. A then draws 3 balls, leaving 4 balls.
- If B draws 2 balls, 6 balls remain. A then draws 2 balls, leaving 4 balls.
- If B draws 3 balls, 5 balls remain. A then draws 1 ball, leaving 4 balls.
3. Final Stage with 4 Balls Left: At this point, no matter how B draws (1, 2, or 3 balls), A will always be able to draw the remaining balls in the next turn. This is because:
- If B draws 1 ball, 3 balls remain, and A can draw all 3.
- If B draws 2 balls, 2 balls remain, and A can draw both.
- If B draws 3 balls, 1 ball remains, and A can draw the last ball.
4. Conclusion: By following this strategy, A ensures that they will always draw the last ball, regardless of B's actions. Therefore, A has a winning strategy.
Hence, the correct answer is .
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