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 Prime Perimeter (Posted on 2005-03-11)

You and two other people have numbers written on your foreheads. You are all told that the three numbers are primes and that they form the sides of a triangle with a prime perimeter. You see 5 and 7 on the other two heads and both of the other people agree that they cannot deduce the number on their own foreheads.

 See The Solution Submitted by Erik O. Rating: 2.8235 (17 votes)

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 re(2): full solution as understood | Comment 21 of 89 |
(In reply to re: full solution as understood by Sachin)

"Scenario 1. A=5, B =5 and C =7

In this case C will see 2 fives which means the only possible values for C are 3 or 7. If C's value is 3, B could have guessed his numbers as he is seeing 3 and 5, and only possible third number is 5. But B couldn't, which leaves C's number as 7. Since even C could not guess his number as 7. So scenario 1 is not possible."

But if B were seeing 3 and 5 he could assume his own was either 3 or 5, not just 5.

"Scenario 2. A = 7, B =5 and C =7

In this case B will see 2 sevens which means the only possible values for B are 3 or 5. If B's value is 3, C could have guessed his number as he is seeing 3 and 7, and only possible third number is 7. But C couldn't, which leaves B's number as 5. Since even B could not guess his number as 5. So scenario 2 is also not possible."

If C were seeing 3 and 7, then 3 would be another possibility for C to consider possible besides the 7.

So is still think it would take at least two rounds of thinking, that included the third person (me, you, depending on who's reading--Yes I mistakenly said narrator before--I meant the person doing this thinking and coming to a conclusion).

 Posted by Charlie on 2005-03-12 03:01:36

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