1000 石头
1000 Stones
题目详情
桌子上有 1000 块石头。两名玩家轮流每轮取下 1、2 或 3 个石子。拿走最后一块石头的玩家就是胜利者。在这场游戏中，第一名还是第二名玩家有优势？
There are 1000 stones on a table. Two players take turns taking off either 1, 2, or 3 stones per turn. The player to take the last stone off is the winner. Does the first or second player have the advantage in this game?
解析
让我们看一下获胜条件，然后将其推断为 1000 颗宝石。如果桌上有 1、2 或 3 颗石子，并且轮到你了，你可以通过消除所有剩余的石子来赢得游戏。因此，我们可以说 1、2 和 3 是“中奖号码”。按照同样的逻辑，4 是一个“输牌号码”，因为无论你做出什么决定，你都会给对手一个赢牌号码。继续下去，我们可以看到所有 4 的倍数都是输数，因此第二名的玩家总是可以通过将对手置于 4 的倍数来保证获胜。
Original Explanation
Let's take a look at winning conditions and then extrapolate that to 1000 stones. If there are 1, 2, or 3 stones on the table and it is your turn, you can win the game by removing all of the remaining stones. Thus, we can say 1, 2, and 3 are "winning numbers". By the same logic, 4 is a "losing number" since you will be giving your opponent a winning number regardless of what decision you make. Continuing this, we can see that all multiples of 4 are losing numbers so the player to go second can always guarantee a win by putting the opponent at a multiple of 4.