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Group theory: Kingdom of Nashville

Question

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The King of Nashville decides to challenge his cabinet of 20 ministers. Each minister has to select a number in the range of 0 and 100 which is 50% of the most likely number selected by other minsters. The king announces that the group will be beheaded if anyone selects a wrong number or will go home with a booty of 100 coins each.

Each minister goes home rich, what number did they select and why?

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The question is definitely flawed but not for the reason mentioned previously.

The question is based on the ASSUMPTION that there exist a "most likely chosen number".

But that assumption may not be correct.

If all the 20 ministers select different numbers than there is no "most likely chosen number" and there is no question of choosing half of most likely chosen number.

And in that case King is in trouble because he has assumed that there will be a most likely chosen number.

Question makes more sense if ministers are at least 100 or more than 100.

Because in that case it is sure that there exists a "most likely chosen number".

Given that not everyone on this board does not have the same high command of English...this makes more sense if the intent was "expected value" (a.k.a average).

Edited by Quantum.Mechanic

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