(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