Unfaithful Wives - Back to the Logic Puzzles
An anthropologist studying a primitive tribe in a remote location in the Amazon basin, had uncovered a strange tribal custom. Whereby, if a husband found out his wife was unfaithful to him, he must execute her in a public ceremony in front of the whole tribe on the same day at midnight. It so happened that every man in the tribe knew about every cheating wife except his own, since telling a man about his cheating wife was against the tribal honor code. On the day of his departure, the anthropologist held a tribal meeting and made the announcement: “I know there are unfaithful wives in this tribe.” On the ninth day thereafter all cheating wives were executed at the same time.
How many unfaithful wives were there?
Spoiler for Solution:
Josephine - solution
The two questions for scroll #1 were:
1. How many husbands were shot on that fateful night?
2. Why is Queen Henrietta I revered in Mamajorca?
The answers are:
If there are n unfaithful husbands (UHs), every wife of an UH knows of n-1 UH's while every wife of a faithful husband knows of n UHs. [this because everyone has perfect information about everything except the fidelity of their own husband]. Now we do a simple induction: Assume that there is only one UH. Then all the wives but one know that there is just one UH, but the wife of the UH thinks that everyone is faithful. Upon hearing that "there is at least one UH", the wife realizes that the only husband it can be is her own, and so shoots him. Now, imagine that there are just two UH's. Each wife of an UH assumes that the situation is "only one UH in town" and so waits to hear the other wife (she knows who it is, of course) shoot her husband on the first night. When no one is shot, that can only be because her OWN husband was a second UH. The wife of the second UH makes the same deduction when no shot is fired the first night (she was waiting, and expecting the other to shoot, too). So they both figure it out after the first night, and shoot their husbands the second night. It is easy to tidy up the induction to show that the n UHs will all be shot just on the n'th midnight.
Spoiler for old wording:
The recent expedition to the lost city of Atlantis discovered scrolls attributed to the great poet, scholar, philosopher Josephine. They number eight in all, and here is the first.
The kingdom of Mamajorca, was ruled by queen Henrietta I. In Mamajorca women have to pass an extensive logic exam before they are allowed to get married. Queens do not have to take this exam. All the women in Mamajorca are loyal to their queen and do whatever she tells them to. The queens of Mamajorca are truthful. All shots fired in Mamajorca can be heard in every house. All above facts are known to be common knowledge.
Henrietta was worried about the infidelity of the married men in Mamajorca. She summoned all the wives to the town square, and made the following announcement. "There is at least one unfaithful husband in Mamajorca. All wives know which husbands are unfaithful, but have no knowledge about the fidelity of their own husband. You are forbidden to discuss your husband's faithfulness with any other woman. If you discover that your husband is unfaithful, you must shoot him at precisely midnight of the day you find that out."
Thirty-nine silent nights followed the queen's announcement. On the fortieth night, shots were heard. Queen Henrietta I is revered in Mamajorcan history.
Edit (implied questions moved from solution to the wording of the puzzle):
The two questions for scroll #1 were:
1. How many husbands were shot on that fateful night?
2. Why is Queen Henrietta I revered in Mamajorca?
I think they should be able to figure out how many unfaithful men there are.
They can just ask eachother how many unfaithful men the other woman knows. If they ever get an answer that higher than their number then their husband is a cheater!
There is one possible weakness in this solution, which you may want to address in an edit or a future post.
If any husband was faithful on the day of the proclamation, but became unfaithful during the first 40 days, wouldn't that throw the logic out of order in such a way as to be impossible to tell the exact number?
Just curious since I haven't actually thought it through and I'm too tired to figure the long term effects.
Sign In
Register
Help
MultiQuote
