In the following statements, each of the capital letters in bold represent a different decimal digit from 1 to 9.

COUSCOUS is an 8-digit positive integer none of whose digits is composite and it is divisible without remainder by each of the primes CU, S, F, CFU and UF but not by the prime number CC.

What is the number represented by FOCUS?

C is obviously 1, as the only prime number CC can be is 11 (else it would be a composite of 11). CFU is then 137 or 173, with S and O as 2 or 5. The only 8-digit, COUSCOUS, divisible by CU, S, F, CFU and UF that is not divisible by CC is 12751275, therefore
FOCUS = 32175.

Posted by Dej Mar on 2008-11-10 21:32:28