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Mixing Digits (Posted on 2004-12-29) Difficulty: 1 of 5
If this sum is correct, what digits do A and M represent? MA + A = AM

See The Solution Submitted by Jim    
Rating: 2.1111 (9 votes)

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re(4): Solution (spoilers) | Comment 7 of 25 |
(In reply to re(3): Solution (spoilers) by nikki)

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
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