updated
This problem contributed by Bahram:
There are 5 pirates who steal 100 diamonds and they want to divide them. They decide to do so as follows:
They create a circle and choose a person by chance so that he assigns diamonds according to his wish. Nevertheless, to have a little more reasoning, they decide to add a second rule: once the division is made, everyone will vote if he is OK with this division or not. If the majority accept the division, then the division becomes final.
Otherwise, they kill the person who made the division, and the next pirate in the circle will do the division with the same rules.
The question is: what is an optimal strategy for the first person,
knowing that everyone would want to maximize his share and that everyone is excellent in logical deduction!
Another thing: when one makes the vote between 5, assuming that he himself votes O.K., 3 negative votes will be regarded as "NO". When one makes the vote between 4, still assuming that he votes O.K., 2 negative votes will be a "NO".
Posted by Shauheen at May 8, 2004 10:37 PM> what is an optimal strategy for the
> first person,
Let me guess:
- to assign 20 diamonds for each and
vote NO to himself??
- to pass the task to the next guy and
commit suicide??
- to take all the diamonds and run away??
> when one makes the vote between 5, ...
so...
3 out of 5 voters,
3 out of 4 veters,
2 out of 3 voters,
2 out of 2 voters,
are needed for an assignment to be approved?
He may give
2 diamonds to the 5th guy in the circle,
3 to the 4th,
1 to the 3rd,
and take the rest for himself.
Let's say they are:
Sir Henry Morgan, Thomas Tew, Francis Drake, William Kidd, Edward Teach
Henry is the first one to decide:
1- He knows thad Edward would say NO.
2- He also knows that William can get mostly 1 piece of diamond. (because if it's his turn he should give all the treasure to Edward), So William would be happy with 1 diamond.
He needs only one other positive vote now. He gives 1 diamond to Thomas.
3- Thomas knows that if he doesn't accept this offer when it is his turn he has no chance of getting any diamond. (because with 4 pirates the first one should give 1 to William and the rest to Francis to gather 2 positive votes)
Henry Morgan takes 98 diamonds. gives 1 to William Kidd and 1 to Thomas Tew.
Not a good day for a gentleman like Francis Drake.
and Blackbeard knew that he would get nothing!
Bravo sir Idin kidd!
I think it should be correct.
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