A workshop in Florida for 2009 Math Kangaroo Competition.
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A = 9
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.
I think 9 since 99+99=198