(In reply to re(3): Solution (spoilers)
Adding the units positions, A+A, results in either M (if there is no carry) or 10+M (if there is a carry), as there can't be a carry larger than 1 (representing 10).
As A is the only item being added, the only way for the M in the ten's position of the first addend to become an A in the sum is for there to have been a carry, so indeed A+A=10+M, rather than just M.
Since the M got transformed into an A as a result solely of the carry, and that carry was 1, M+1=A, or M=A-1. The solution of these simultaneous equations was then in my first post.
Posted by Charlie
on 2004-12-29 16:43:19