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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 2, 2005 4:39 PM
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Sylvain Croussette answered on alt.math.undergrad:
> st9468s4 (EJC) wrote:

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

Assuming A,B and C are single digits:
Rewrite as:

>From the 1st column: B+A=C, or B+A=C+10, if there is a carry.
From the 2nd column also A+B=B; this is the same as the 1st column
so it's impossible, unless there is a carry from the 1st; so it's
1+A+B=B+10, because A+B produced a carry in the 1st column.
From the third column 1+C+C=A.
Rewrite these equations:
1) A+B-C=10
2) A+B-B=9
3) A-2C=1
Clearly from equation 2, A=9, so from equation 3, C=4 so B=5.

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