Prof. Giray Okten

Wednesday, February 18, 2009

Challenge Problem

In the addition problem below, different letters represent different digits. What digit does A represent?

    A A
+ A A


  1. In the ones column, A+A=B (with possibly a carry of ten)
    In the tens column, A+A (+1?) = CA.
    Since A is a one-digit number, CA must be between 10 and 19, so C is 1.
    Since 2A is a two-digit number, A must be greater than 4. Also, since 2A + 1 = CA, A must be an odd number.

    So A must be 5, 7, or 9.

    If A is 5, 2A+1=11, which makes CA = 11. That would mean A is both 5 and 1. So A can't be 5.

    Likewise, if A is 7, 2A+1=15, which means A is both 7 and 5. Not possible.

    That leaves 9 as the only possible value for A. Checking: 9+9+1=19. Yes, that works.

    So the answer is that A=9.