Enigma
The British science weekly New Scientist runs a puzzle every week. The current puzzle is this:
The letters of EIGHTMAN represent different digits. When representing a number, ENIGMA is the product of GGG and TTT. Furthermore, a six-digit number using the letters of ENIGMA in a different order is the product of GGG and HHH.
Please send in the number EIGHTMAN.
I think this should be fairly easily amenable to an exhaustive search. There are only 72 possibilities for GGG and TTT (each is a digit from one to nine and different so 9 × 8 combinations). I expect that this would produce several possibilities — there would need to be at least two.
Why would there need to be at least two?
Another way to solve it would be to simply try all the eight digit combinations for EIGHTMAN and look for a match.
How many combinations would this program need to check?
Of course if you get an answer to the actual problem then don't tell me, tell the New Scientist and maybe you can win £15! — if you do win, remember you owe me a beer for my help :)
