The missionary.

Sean · Guest

I'll tell you about the missionary. The answer is somewhat involved but if you give it your full attention you will be amply rewarded by the elegance and completeness of the solution.

There was a remote tiny island that a missionary was visiting and whose people maintained rigidly two ancient traditions. Firstly if a woman was cheating on her husband, the lucky man (or woman!) would tell everyone on the island except the woman's husband and no one would tell the husband. Secondly if a husband found out that his wife was cheating on him he would take her out into the town square at midnight that night and hang her, leaving her body strung up as a warning to any would be wayward wives.

Now the people of this island had the benefit of a missionary who was saving their heathen soles for the past six months and now he was down on the jetty ready to push off. All the islanders had gathered to bid him farewell. The last words the missionary said to them were "there has been cheating going on this island". Now the question is what happened on the island?

Guest · Posted: Fri Sep 23, 2005 11:51 pm Post subject:

cheating?

renee146blah · Guest

well, if there had been two cases of cheating, then nothing would happen, because both men who only knew of the other man's misfortune would assume that the remark was made in reference to that... this applies for more than two cases as well...

however...
if there had only been one instance of cheating, then there would be one man who did not know of any cheating... assuming that he has a decent brain, he would be able to deduce that his wife had been cheating, and so he would hang her at midnight Very Happy

Sean · Guest

If there were two cases would each man who only heard of one case not expect to see that woman hung in the town square the following morning? And if she wasn't hung what would he think then (assuming he had half a brain?)

poisonousfungus · New Member Joined: 02 Sep 2005 Posts: 5

The missionary said "There is cheating going on on this island" to everyone, but he did not take any names. Note that he told everyone, not anyone was excluded. This, and the fact that he did not take any name means that all the wives on the island had cheated, and the missionary was the lucky man. If the folks on the island figure this out, then that midnight all the wives would have been hung at the town square.

This is my take on it. What do you think?

no one · Guest

deduce...hehehe Surprised

but i agree with poisonousfungus

Sean · Guest

If all the wifes were cheating then indeed they all would be hung, but on what day? The information you are given does not state that all the wifes were cheating therfore you cannot assume it.

Guest · Guest

so whats the answer?

Sean · Guest

If only one woman was cheating, there would be only one man in the crowd that had not heard of any woman cheating. He would then conclude that it must be his wife the missionary was talking about so, given the traditions, he would take her out and hang her at midnight.

Now if two women were cheating, two men in the crowd would only have heard of one fornicator and assume that the missionary was talking about the other man's wife, and he would expect to see that wife hanging in the town square the next morning. However, when he doesn't see her he can only assume that the other man did not hang her because that man must also know of a woman cheating. Now given that the first man only knows of one woman cheating, he must come to the conclusion that the reason that woman wasn't hung is because his own wife is cheating also. Both men, having reached this sad conclusion, will then take their respective wives out into the town square on the second night and hang them. This logic will also follow through for any number of 1 to n women (they will be hung on the nth night). The maths never left me!

The solution also covers the unlikely event of the missionary being mischievous and lying to the islanders. If that is the case and no one is cheating then no one will have been told of a woman cheating and they will all assume that their wife is cheating. They will all then turn up in the town square at midnight the first night, realise what has happened and they will all then go home with a weight off their minds.