# Explanaion of Letter Equation

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Please explain:

ABCDE X 4 = EDCBA

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#### Solution Preview

Assume that A, B, C, D and E can only be one of ten numbers 0,1,2,...,9. We solve this equation as follows.

Since ABCDE *4=EDCBA (*)

we know that A must be an even number, i.e, A may be 0,2,4,6,8. Obviously, A can't be 4,6,8 since otherwise, ABCDE*4>100000 which is impossible. So we consider the following two cases.

(1) A=2

By (*) we know that E=8. So we can write (*) as follows.

2BCD8*4=8DCB2,

that ...

#### Solution Summary

This shows how to assign numbers to letters in a multiplication problem.

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