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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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Solution Problem Solution : Method III | Comment 23 of 25 |
(In reply to Problem Solution : Method II by K Sengupta)

Rewriting the equation as:

AM - MA = A, we obtain:
9(A-M) = A.....(*)

Clearly, A and M cannot be equal as these must denote separate digits.

If A- M >=2, the rhs in (*) contain more than one digit. Contradiction.

If A- M <= -1, then rhs of (*) is negative, which is a contradiction.

Accordingly, A-M =1, giving A =9, so that M =8

Consequently, M and A respectively represent the digits 8 and 9.

Edited on August 24, 2007, 6:22 am
  Posted by K Sengupta on 2007-08-24 06:21:33

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