Alice, Betty and Carol each chose two 2-digit semiprimes (products of exactly two primes each) whose difference was also a semiprime. In each of the three cases, the six primes going into the three semiprimes involved were all different. Also in each case, the sum of the two semiprimes was a perfect square.

Alice, Betty and Carol had different pairs of semiprimes, though there may have been repetition of any given semiprime. Alice and Betty had the same sum for their semiprimes, but Carol's sum was different.

What were Carol's two semiprimes?

(In reply to re(2): Solution - Interpretation? (spoiler) by Dej Mar)

Thank you Dej Mar.

I failed to properly understand the true implication of: "In each of the three cases,".  Consequently I was looking at the semiprime for each case which formed the difference, not the three semiprimes for each instance.

Yes, it's all clear to me now.

Posted by brianjn on 2011-04-13 05:15:57