If A*BCDEF=GGGGGG, and each different letter stands for a different digit, what's G?

A * BCDEF = GGGGGG

GGGGGG = G * 111111 = G * (3 * 7 * 11 * 13 * 37).

Thus, A * BCDEF = G * 3 * 7 * 11 * 13 * 37, and so A must be either 3 or 7.

But if A = 3, then BCDEF = G * 37037, giving BCDEF = 37037 if G = 1, or BCDEF = 74074 if G = 2 (for G > 2, the product has more than 5 digits); impossible, repeating digits. Thus A = 7.

So BCDEF = G * (3 * 11 * 13 * 17) = G * 15873.

Since each letter stand for a different digit, a quick check gives:

G = 2 ----> BCDEF = 2 * 15873 = 31746 (no, A is already 7)
G = 3 ----> BCDEF = 3 * 15873 = 47619 (no, A is already 7)
G = 4 ----> BCDEF = 4 * 15873 = 63492 (no, G = 4)
G = 5 ----> BCDEF = 5 * 15873 = 79365 (no, G = 5)
G = 6 ----> BCDEF = 6 * 15873 = 95238 (possible)

For G > 6 the product has more than 6 digits.

Thus the only answer is G = 6, and BCDEF = 95238.

7 * 95238 = 666666.

Posted by pcbouhid on 2005-11-18 07:43:29