A seven digit positive

**octal** integer

**X** is constituted by arranging the nonzero octal digits 1-7 in some order, so that:

- The octal number formed by the first two digits is divisible by 2.

- The octal number formed by the first three digits is divisible by 3.

- The octal number formed by the first four digits is divisible by 4.
- and, so on up to seven digits...

Determine all possible value(s) that

**X** can assume.

(In reply to

computer solution by Charlie)

Charlie, I understood this problem differently--I thought the first two digits would be the rightmost digits. I got all excited that you were totally wrong (the number has to end in 4--none of those values can work!) and then I realized that one of us got it backwards. But which one?!

In any case, I had some fun working out rules of divisibility in base 8. That is, until I got to 5.

I think that, for my way, 6732154 works, but I don't want to double-check my work, and I don't want to have to find another value. Like I said, dividing by 5 in base 8 is no fun.