# Numerical puzzle

## Homework Statement

Im having problem of even starting this question:

"Determine the positive integer N = abcdef such that 6N = defabc"

any ideas?

## The Attempt at a Solution

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$$6N = defabc = abcdef = N$$

6N doesn't equal N unless it's 0. The only solution is 0 which is not a positive integer.

Or am I missing something really stupid?

actually i ended up solving it
abc = 142 and def = 857

....abc and def are just the digits in the question. but thanks!

dynamicsolo
Homework Helper
Actually, anyone who recognizes the decimal expansions of 1/7 and 6/7 might suspect immediately that this is an answer... (Ah, but is it unique?)

Feldoh, this type of puzzle is what is referred to as a cryptarithm. Letters stand in for digits and the prospective solver is supposed to "decode" the arithmetic problem. In classical form, this problem would be posed as

ABCDEF
x 6
______
DEFABC

The question does not say that 6N = N , but that 6N is a digital rearrangment of N.

Regardless I think the question could be worded better...

dynamicsolo
Homework Helper
It did strike me that the intent of the problem might be obscure to anyone not familiar with this kind of puzzle.