Beware Of Extended Vacations On The Islands
- 2
- Add a Comment
- No Related Post
Here is a logical puzzle I found in similar versions in several places. As always, I claim no authorship, but I am presenting my own retelling of what must be a mythical story. If anyone knows the actual originator on the underlying puzzle, let me know, and I will give credit where credit is due.
Assume a remote island that has a community of castaways living on it. The various versions of this puzzle have different numbers of people, but we know that our island has exactly 40 couples and no children. Since this is a remote island, there is no HDTV, Internet, ESPN, motocross, etc. This creates a generally boring life. Naturally partners in the various couples started to mess around with others. The women called the men cheaters who did it, but strictly speaking, the women who did it were cheaters also. The main difference was that each woman had a pistol, and the men had none. This also naturally led to one of the women being elected as grand ultimate leader of the island.
Again, for reasons that I do not understand, the leader felt that men who cheated should be punished. She didn’t say anything about the women who did the same thing, but then the other women all had pistols. She thought about this intolerable situation for some time. She thought about it while walking around and listening the inevitable gossip that flows freely in an isolated group like her small country.
Then one day she realized an important fact about the cheating. It could be solved. She called a convocation of all the women. She started by saying there was cheating going on and it must be stopped. She said that while listening to chatter, she came to realize that all the women on the island knew which men were cheating except they did not know if their own mates were cheating. This was because the gossipers would not pass on that information to the harmed woman, and the men were not talking. Therefore she made a new decree. Effective immediately, no woman could discuss with any other person whether or not her mate was cheating. However, if any woman discovered that her mate was a cheater, she must shoot him at sundown on the day she made the discovery.
The couples re-united (men had been excluded from the meeting) and went to their huts. At sundown no shots were heard and everyone went to sleep. The same thing happened the next day and the next.
To understand the nature of this puzzle, please put aside any questions of why no rescue ship arrived to whisk the couples back to civilization. After all, the Minnow stayed aground for years only a few hours’ cruise from shore while Gilligan aged perceptibly with no rescue.
Time passed.
At the fortieth sundown, shots were heard. Why then and how many men were shot? Were any innocent men shot in error, or were any guilty ones mistakenly spared?
That’s the main puzzle. For extra credit, what did people talk about at dinner the next day?
As always, the answer to the main puzzle will be posted next week. The extra credit puzzle can have many answers. I will post samples of the best that readers submit — if more than one is submitted.
In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.
[tags]puzzle, logic, decision theory[/tags]
2 Comments
Robert W Gilcrease
April 27th, 2007
at 10:28am
I’ve been asked to produce a basic html, web design course for seniors in our Adult Learning Center. I’m writing to ask your advice as to what I should include in the course work, for those who are not real computer savy. Please, I would love to read what you think should be covered in this course work.
BC
May 3rd, 2007
at 6:14pm
How amusing. I just read your May 2 post in my e-mail, and tabbed over here to find that I never submitted. Oh well, just for the fun of it, here’s the response I wrote, and you’ll have to take my word for it that I wrote it before the second.
——————————
I really dislike induction puzzles, because they assume not just perfect and timely reasoning on the part of everyone involved, but the assumption of perfect and timely reasoning of everyone involved, *by* everyone involved.
This one is essentially Josephine’s Problem. The reasoning goes like this:
If there were only 1 unfaithful husband, then every woman on the island would know that except for his wife, who would otherwise believe that everyone is faithful. Thus, as soon as she hears from the leader that unfaithful men exist, she knows her husband must be unfaithful, and shoots him.
If there are 2 unfaithful husbands, then both their wives believe there is only 1 unfaithful husband (the other one). Thus, they will expect that the case above will apply, and that the other husband’s wife will shoot him at sundown on the next day. When no gunshot is heard, they will realise that the case above did not apply, thus there must be more than 1 unfaithful husband and (since they know that everyone else is faithful) the extra one must be their own husband.
If there are 3 unfaithful husbands, each of their wives believes there to be only 2, so they will expect that the case above will apply and both husbands will be shot on the second day. When they hear no gunshot, they will realize that the case above did not apply, thus there must be more than 2 unfaithful husbands and as before their own husband is the only candidate to be the extra one.
In general, if there are n unfaithful husbands, each of their wives will believe there to be n-1 and will expect to hear a gunshot at sundown on the n-1th day. When they don’t, they know their own husband was the nth.
And so, since there was no carnage prior to the 40th sundown, then every husband was unfaithful, and every one was shot. Making, of course, the assumptions of not only perfect logic and timing of every woman involved, but their willingness to presume the same of each other.
I presume that dinner conversation the following night revolved around every woman determining who her husband was cheating with, as politely as possible.
Then, of course, they’re likely to determine that they don’t actually live in “Logicland” and the human condition means that it’s entirely possible that one or more of them shot an innocent man.