 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  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) Comments: ( Back to comment list | You must be logged in to post comments.) full solution | Comment 7 of 89 | Since the numbers are the sides of a triangle, my number is between 3 [ > (7-5)] and 11 [ < (7+5)]. So my number (a prime) could be only 3, 5, 7 and 11.

My number couldn't be 3, because the perimeter (3 + 5 + 7) = 15, isn't a prime.

If my number is a 5, the one that have a 7 will reason : "I'm seeing two 5's, and so my number is a 3 or a 7 (remember the prime perimeter). If my number is a 3, then the other two could deduce that both have a 5, since if one of them had a 3, the other would know that he had to have a 5. Since no one announced his number, my number is not a 3, so my number is 7". Since the one that have a 7 didn't say nothing, my number is not a 5.

If my number is a 7, the one that have a 5 will reason : "I'm seeing two 7's, so my number is a 3 or a 5 (remember the prime perimeter). If my number is 3, the other two would know that they both had a 7, and since no one announced nothing, my number is a 5". Since the one that have a 5 didn't say nothing, my number is not a 7, too.

So, my number is 11.

 Posted by pcbouhid on 2005-03-11 19:27:14 Please log in:

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