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: Solution - Interpretation? by brianjn)

Regarding your concern, the meaning of the sentence "In each of the three cases, the six primes going into the three semiprimes involved were all different." may be more clearly shown by the following:
Semiprimes: 21, 74, 95
Six Primes: 2, 3, 5, 7, 19, 37
            74 = (2 * 37)
            95 = (5 * 19)
|74 - 95| = 21 = (3 *  7)

Semiprimes: 35, 51, 86
Six Primes: 2, 3, 5, 7, 17, 43
            35 = (5 *  7)
            86 = (2 * 43)
|35 - 86| = 51 = (3 * 17)

Semiprimes: 26, 69, 95
Six Primes: 2, 3, 5, 13, 19, 23
            26 = (2 * 13)
            95 = (5 * 19)
|26 - 95| = 69 = (3 * 23)

Posted by Dej Mar on 2011-04-13 04:56:24