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Prime Perimeter (Posted on 2005-03-11) Difficulty: 3 of 5

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.

What is the number written on your forehead?

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(2): Charlie's Skepticism | Comment 33 of 89 |
(In reply to re: Charlie's Skepticism by Charlie)

I agree mostly. I think Erik's problem would be more clear and even more fun if it included a story about the capability of the folks at the table, the time elapsing, and perhaps even some stakes. I think it is an omission to not imply that "You" do not have an known incentive for solving the riddle at all (or even being honest).

Still, I really don't think it is "too many levels of logic" to recognize that if one of the three parties were in fact viewing a pair of 5's or 7's that they couldn't deduce their own number. And certainly they wouldn't agree (give up) that they cannot deduce their own number if they were only wrestling with wether they have a 3 or not. Giving up is only likely when they are faced with scenarios 7,11 and 5,11 both of which have three viable solutions and even deep logic tests cannot reduce them.

Especially if we grant a little to the constructed nature of logic problems.
  Posted by Eric on 2005-03-12 17:00:06

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