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Topic: Finding A, B, and C
Replies: 4   Last Post: Jan 21, 2005 6:12 PM

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Nat Silver

Posts: 2,082
Registered: 12/6/04
Re: Finding A, B, and C
Posted: Jan 21, 2005 6:12 PM
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Laura Haliman writes:

> ABC I have to find the values of A, B and C where A>B>C
>- CBA
>= CAB

The subtraction ABC - CBA = CAB
can be rewritten in an equivalent form
using addition: CAB + CBA = ABC.


Let's add. We add the right column of numbers first:
A+B = C or if A+B were larger than 9, we would have a carry of 1.
(Remember, the 1 is really a ten. It is in the tens' column.)
In that case, we would know that A+B = 10 + C.

Let's add the middle column of numbers.
It's A+B again. If there were no carry, it would have to
be A+B = C, but A+B = B. So, there was a carry afterall.
And, actually, A+B = 10 + C.

Because we now know that A+B is larger than 9, and because
we also know there is a carry of 1, from the middle column, we
get: 1+A+B = 10+B, which reduces to: A = 9.

We still know that A+B is larger than 9.
So a 1 was carried into the left column from the middle column.
We have 1+C+C = A. But A = 9.
Then, 2C+1 = 9 ==> C = 4.

Backtracking to A+B = 10+C, and substituting
gives us 9+B = 10+4 ==> B = 5.

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