 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.) re: full solution as understood | Comment 20 of 89 | (In reply to full solution by pcbouhid)

From what I have understood from pcbouhid solution. There are three possible numbers for,say for  A as 5,7,11. Let say B has 5 and C has 7.

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.

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.

So we are left with the only possible values of A = 11, B =5 and C =7.

So the number is 11.

Edited on March 12, 2005, 2:12 am

Edited on March 12, 2005, 2:13 am

Edited on March 12, 2005, 2:17 am
 Posted by Sachin on 2005-03-12 02:00:00 Please log in:

 Search: Search body:
Forums (2)