15. (12 points) A and B play a matchstick game, with a total of 10 matchsticks on the table. The one who takes the last matchstick wins. A can take 1, 3, or 4 matchsticks each time (only the exact number can be taken; if there are 2 matchsticks left, A can only take 1), and B can take 1 or 2 matchsticks each time. If A goes first, to win, A should
Problem 464
Pick one
Official solution
【Answer】Solution: No matter how player A moves, player B just needs to ensure that there are two matches left at the end, at which point player A can only take 1 match, and player B wins; before this, as long as there are 5 matches left, if player A takes 1 match, then player B takes 2 matches, leaving 2 matches, and player B wins; or if player A takes 3 matches, player B takes 2 matches, and player B wins; or if player A takes 4 matches, player B takes 1 match, and player B wins. Therefore, no matter how player A takes, they cannot win. Hence, the answer is: D.