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tijanoo's avatar

how many wise men has come forward?

Asked by tijanoo (1points) November 22nd, 2007

king has collected all the wise men of the world and on someone’s back has put a diamond and on someones emerald. all of them had something on their back but they couldn’t see what is on them. king said once: let all of wise men with diamond on their back come forward. no one came forward. the same thing hapend the second and the third time.. when the king said it for the fourth time all wise men with diamonds on their back came forward. how many did came forward and why?

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2 Answers

iomar's avatar

One came forward becouse there are only two wise men.

chris's avatar

four wise men came forward. As usual with these riddles, the way to go is to work up from the case easy case and each time add one.

A – If only one man has a diamond, then he sees that all the other men have emeralds, so he steps forward the first time. A ends in 1.

B – If two men have diamonds, then the first time, they don’t step forward because it could be the case that the other person has the only diamond. But if that person doesn’t step forward the first time, then they know that we are not in situation A, which is over after one time, so they step forward the next time. B ends in 2.

C – three men have diamonds. They each see two other men with diamonds. This means that after the question is asked twice, they know we are not in case B, so on the third time they step forward. C ends in 3.

D – four men have diamonds. They see three others with diamonds, so have to decide between case C (dont step forward) and case D (step forward). After the third time, no one has stepped forward, so C is ruled out. They step forward the next time. D ends in 4.

this proceeds by induction to the case with an arbitrarily large number of men with diamonds.

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