Puzzle 69 - Solution

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The question was

In the following subtraction problem, each letter uniquely repre- sents one digit from 0 to 9. At least one digit is not 0. Find the values of A, B, and C.

ABA – CA= AB

 Now if A, B and C represent digits from 0 to 9, the following equation will be

100A+10B+A - (10C+A) = 10xA+B

 90A+9B = 10C 

9(10A+B) = 10C

10A+B = 10/9 C

 To have integer values for A and B, C has to be 9. By replacing C with 9 we get,

10A+B = 10

If A and B have to between 0 to 9, A has to be 1 and B has to be 0.

So A =1, B = 0 and C=9

 

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