Ann and Bob are playing on the beach.安和鲍勃正在海滩上玩耍。
Ann has collected many light colored shells, Bob has collected many dark colored pebbles.安收集了许多浅色的贝壳，鲍勃收集了许多深色的卵石。
They made holes in the sand and connected them with furrows.他们在沙地上挖了一些洞，并用沟渠把它们连了起来。
They then take turns to put one of their items in an empty hole.然后他们轮流将自己的一件物品放入一个空洞中。
The loser is the first player to place two of their pieces into two holes connected by a furrow.输家是第一个将两枚棋子放入由一条犁沟相连的两个洞中的玩家。
Ann started the game. They have reached the position shown in the figure below. It is Ann's turn.安开始了游戏。他们已到达如下图所示的位置。现在轮到安了。
Question:问题:
In which empty hole must Ann place a shell to ensure victory for herself?安必须把贝壳放在哪个空洞里才能确保自己获胜？
(Click on it and then press 'Save.')（点击它，然后按“保存”。）
Explanation 解释
Answer: 答案:
Hole number 7. 7号洞。
Explanation: 解释:
Holes 1, 3, 4 and 6 are "closed" to Ann; holes 1, 4, 5 and 6 to Bob. After Anna has put a shell in 7, Bob can play either 2 or 3; in both cases, Ann just puts a shell on 5 to force Bob to lose.对于安来说，1、3、4 和 6 号洞是“封闭”的；对于鲍勃来说，1、4、5 和 6 号洞是“封闭”的。安娜把贝壳放在 7 号洞后，鲍勃可以放 2 号洞或者 3 号洞；无论哪种情况，安只需把贝壳放在 5 号洞就能迫使鲍勃输。
If, from the position shown in the figure, Ann had put a shell in 2, the game would have continued in this way: Bob 7, Ann 5, Bob 3, and Ann loses.如果从图中所示的局面开始，安在 2 位置放了一枚贝壳，那么游戏会这样继续：鲍勃放 7，安放 5，鲍勃放 3，安就输了。
Finally, if Ann had put a shell in 5, the game would have continued in this way: Bob 7, Ann 2, Bob 3 and Ann loses again.最后，如果安在 5 这个位置放了一枚贝壳，游戏就会这样继续：鲍勃 7，安 2，鲍勃 3，安再次输掉。
It is interesting to note that, in the position shown in the figure, if it were Bob's turn, Bob would lose anyway. In fact, if Bob occupies either 2 or 3, Ann occupies 7; instead, if Bob occupies 7, Ann occupies 2, then Bob 3 and Ann 5.有趣的是，在图中所示的位置，如果轮到鲍勃走，鲍勃无论如何都会输。实际上，如果鲍勃占据 2 或 3，安就会占据 7；相反，如果鲍勃占据 7，安占据 2，那么鲍勃占据 3，安占据 5。
But there is another fact, even more interesting: from the initial (empty) board, Bob - who plays second - had a winning strategy... but he made at least one mistake! If Ann's first move was the shell on the left, Bob's top pebble was good (while the bottom one led to a draw) and the mistake occurred on his next move. If, on the other hand, Ann started with the shell on the right, both of Bob's moves were wrong... The task of completing the analysis is yours!但还有一个更有趣的事实：从初始（空的）棋盘开始，后手的鲍勃其实有必胜策略……但他至少犯了一个错误！如果安的第一个棋步是左边的贝壳，鲍勃把石子放在上面是好的（而放在下面则会平局），错误出现在他的下一步。相反，如果安从右边的贝壳开始，鲍勃的两步棋都是错的……完成分析的任务就交给你了！
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