Answer: EIGHTMAN is 28763415
The winner is Alan Beasley of Monkland, Herefordshire, UK. There were 287 entries.
Worked answer
ENIGMA must be a multiple of 111 x 111 = 12321.
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There are 8 x 9, or 36, multiples that need to be considered* (See note below).
Of these, 16 can be rejected, without being explicitly worked out, for being too small (5 digits only) or because A would be a repeat of G or T in the equation ENIGMA = GGG x TTT (1)
Of the remaining 20, only four have all digits different and, of these four, only when ENIGMA = 258741 with G = 7 (and T = 3), is G consistent in (1).
(* It is also possible to use just the + key on a calculator with 12321 as the constant to obtain the unique solution for G & T given above.)
By elimination, H = 0, 6, or 9. H is clearly not 0, and, if it were 9, G x H would end 3 (= T).
So H = 6, as confirmed by 777 x 666 = 517482, and thus EIGHTMAN is 28763415.
