If a, b, and c are different numerals between 1 and 9 (inclusive), and

aaaaaa = b * c * bc * (c+c-b) * (c+b+b) * (c-b),

what are a, b, and c?

**Note:** Adjacent numerals are multi-digit numbers made of those numerals, not the product; i.e., if m=2 and n=3, then mn=23.

aaa,aaa= aaa x 1001 = a x (3x37) x (7x11x13) so one of b, c, bc, c+c-b, c+b+b or c-b must equal 37 or 74. The only possibility is bc=37, since bc=74 would make c-b negative. Doing the numbers, a=4.