2015年Bebras挑战练习题-Pirate Hunters（海盗猎人）

In the game of Pirate Hunters players take turns moving a Pirate or a Policeman.在“海盗猎人”游戏中，玩家轮流移动海盗或警察。

When it is the police's turn, the player moves a policeman over to a neighbouring field.轮到警察时，玩家将一名警察移至相邻的区域。

The pirate is faster than a policeman, and skips a field on its turn, moving two fields.海盗比警察快，在其回合时能跳过一格，移动两格。

A policeman cannot move to a field that is occupied -- either by his colleague policeman, or the pirate.一名警察不能移动到已被占据的区域——无论是被他的同事警察占据，还是被海盗占据。

The game ends when the pirate is forced to move to a field occupied by one of the policemen.当海盗被迫移动到一名警察所在的场地时，游戏结束。

The policeman goes first.警察走在前面。

Question: 问题:

If the pirate plays the best way possible and makes no mistakes, how many moves will it take the police to capture him?如果海盗以最佳方式行动且不犯任何错误，警察需要多少步才能将其抓获？

A. The police can win in 2 turns.

B. The police can win in 3 turns.

C. The police can win in 5 turns.

D. The police has no chance of winning.

 

 

 

 

 

Explanation 解释

The answer is: The police cannot win the game if the pirate plays perfectly.

答案是：如果海盗玩得完美无缺，警察就赢不了这场游戏（选项D）。

Let us assume that the police actually forced the pirate into the above situation and it is the pirate's turn (so he loses). What did the board look like before the police's last move? The police moved one or the other policeman up or down. Since the board is symmetric, we shall assume that it was the right policeman that moved; the situation for the left one is the same. Thus the previous situation was one of these.

我们假设是警方迫使海盗陷入上述局面，且轮到海盗走（所以海盗输了）。警方的上一步棋之前棋盘是什么样子的？警方移动了其中一名警察向上或向下。由于棋盘是对称的，我们假设移动的是右边的警察；左边警察的情况是一样的。因此，之前的局面是这样的。Let us go one more move back. The pirate must had come from the right. Hence the situation before that was one of these two:

让我们再回溯一步。海盗必定是从右边来的。所以之前的情况必然是这两种之一：The above situation, in which the pirate is captured, can therefore arise only from these two positions (and their mirrored versions). However, if the pirate is indeed a good player and found himself in one of these two positions, he would surely move the pirate to the left and not up.

上述海盗被擒获的情况因此只能从这两个位置（及其镜像位置）产生。然而，如果海盗确实是个高手，发现自己处于这两个位置中的任何一个，他肯定会把海盗向左移动而不是向上移动。