# Numerical puzzle

1. Jul 8, 2008

### furnis1

1. The problem statement, all variables and given/known data
Im having problem of even starting this question:

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

any ideas?

2. Relevant equations

3. The attempt at a solution

2. Jul 8, 2008

### Feldoh

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

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?

3. Jul 8, 2008

### furnis1

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

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

4. Jul 8, 2008

### dynamicsolo

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.

5. Jul 8, 2008

### Feldoh

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

6. Jul 8, 2008

### dynamicsolo

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