猜對 保性命

四位囚犯面向同一方向排隊, 第一位囚犯A與其他三位囚犯被一道堅固的磚牆隔開來.

每一位囚犯都戴著一頂帽子, 四頂帽子中兩頂是黑色, 兩頂是白色, 但沒有人知道自己戴什麼顏色的帽子, 也不允許彼此交談, 回頭, 或換位. 他們只能站在原地往前面看.

題目來了, 每位囚犯都會被處決, 除非他在十分鐘內答對他所戴帽子的顏色.

請問, 是哪一位囚犯逃過一劫(答對顏色)? 答案在下面這段原文題目後面.

The “four hat” riddle

Also called the “prisoner hat” riddle, the “four hat” riddle begins with four prisoners who have all been lined up, one behind the other and all facing in the same direction. The first (prisoner A) has been separated from the others by an impenetrable brick wall. The others (prisoners B, C and D) have all been lined up facing the brick wall. Each of the prisoners is wearing a hat. Two of the hats are white, and two are black, but no one knows the color of his own hat.

Now, here’s the sinister kicker: All the prisoners will be killed unless one calls out the correct color of his own hat within 10 minutes. The prisoners are not allowed to confer with one another, nor are they allowed to move around or change position.

Fortunately for all, just before the stopwatch strikes 10 minutes, one prisoner correctly calls out the color of his own hat. Your job, should you accept the challenge of the “four hat” riddle, is to figure out which prisoner it was.

答案是: C 囚犯

如果沒有猜對, 原文說明如下, 若不想看原文, 請跳到最後面的中文說明.

The explanation

As vexing as it might seem, the “four hats” riddle can be solved using the process of elimination. And two of the prisoners (prisoners A and B) can be eliminated right off the bat. That’s because neither can see any of the other prisoners, so neither possesses any information with which to make an educated guess.

That leaves just prisoners C and D.

Prisoner D might seem the obvious choice because he can see the hats of both prisoners C and B in front of him, whereas prisoner C can see only the hat of prisoner B. Indeed, if prisoners B and C were wearing the same color hat, then prisoner D would have known immediately that he was wearing the other color. However, in this scenario, prisoners B and C are wearing different colored hats. Seeing this, prisoner D, in effect, has no more information than prisoners A and B. Accordingly, he too is left in the position of being unable to make an educated guess.

As for prisoner C, prisoner D’s silence is all the information he needs. Had prisoner C and prisoner B been wearing the same color hat, prisoner C surmises, then surely prisoner D would have piped up with the answer already. Accordingly, at the end of the 10 minutes, prisoner C deduces that he and prisoner B must be wearing different color hats. And since prisoner C can see that Prisoner B is wearing a white hat, then prisoner C knows that he must be wearing a black hat.

中文說明:

先用用刪去法, A 與 B 一定不會知道自己戴了什麼顏色的帽子, 所以刪掉 A 跟 B.

D 乍看是最有可能答對的人, 但 D 沒出聲, 這給了 C 很重要的資訊, C 看得到 B 戴白色帽子, 如果C 跟 B 戴相同顏色的帽子, D 一定馬上可以答出來, 所以 C 知道自己一定是戴黑色帽子.