Re: Another Logic Puzzle
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I might be wrong, but I don't think there's enough information here for Logician C to be able to say "my number must be 50" - assuming of course he really is a "perfect" logician.
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This is part of the information that we're given to help solve the problem. The fact that he was able to conclude this helps us solve the problem.
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Another poster said that C would know that he was 50 because if B saw 20 and 10, then he'd know that he was 30 because you can't duplicate the 10. Ok... fine... but who says B didn't see 20 and 11? B could see 20 and 11 and then not know if he was 9 or 31. C doesn't know what's on his forehead, and I'm assuming the 3 individuals are not allowed to share information. C has no idea what B saw, and thus can't act on that information.
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Suppose A has 20 and C has 11. We have two possibilities: Either B has 9 or he has 31.
Case 1:
A=20
B=9
C=11
There's no way for A or B to deduce what their number is. And when it's C's turn to act, there's no way for him to determine whether he has 11 or 29. Since C can't determine this, we know that (20,9,11) isn't a possible solution.
Case 2:
A=20
B=31
C=11
Same thing here. Nobody is able to deduce what number they have, so it's not a possible solution.
Most integer solutions won't work for this reason. In order for C to be able to say for sure what his number is, he has to have the information that either A or B would have been able to guess their numbers had they been something else.
I've seen this problem before, but I'm yet to see a proof of the uniqueness of this solution. So your questions are valid.
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