Solution to Enigma No. 1575

Answer: 528,941

The winner is Doug Fenna of Ryde, Isle of Wight. There were 173 entries.

Worked answer

Since there is no zero, F must be 5.

W can only be 3, since 6 and 9 are divisible by 6 and 9 respectively. MO must be prime.

TU must be even, so SU must be even.

For SU, two-digit even multiples of 7 (which must not include 7 × 8) are 14, 28, 42, 84 and 98.

For SA, two-digit multiples of 6 (but not by 7, 8, or 9) and not including zero are 12, 18, 24, 36, (66), 72, 78, 84 and 96. But 18, 36 and 72 are divisible by 9; 24 and 96 are divisible by 8; 84 is divisible by 7. So SA can only be 12 and thus SU = 14.

Hence, S = 1, A = 2, W = 3, U = 4 and F = 5.

TH is a multiple of 4 (but not 20, 24, 28, 32, 36) and not 40, 44, 48, 52 because U = 4 and A = 2.

56, 60, 64, 72, 80, 88, and 96 are divisible by 8; 60 and 80 contain 0; 68 is possible, 76 is possible, 84 is divisible by 7, 92 contains 2, and 96 is divisible by 6.

If TH = 68 then TU (even) could only be 64 since 62 contains 2, but 64 is divisible by 8. So TH = 76 and TU = 74.

Hence, S = 1, A = 2, W = 3, U = 4, F = 5, H = 6 and T = 7.

Digits remaining are 8 and 9, and the letters unassigned are M and O. MO is prime.

83 and 89 are prime, but W = 3 and 98 is not prime. Therefore M = 8 and O = 9. Therefore, FAMOUS = 528,941.