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.

Considering the necessary conditions of dividing even numbers- our solution in terms of parity must have the structure of **OEOEOEO ,** thus forcing a relatively short list of possible beginnings::<o:p></o:p>

12,32,52,72,14,34,....76.<o:p></o:p>

I used Multiplication And Division of

Octal Numbers Calculator (on the web) to get the next digit, getting the candidate triplets: 127 325 523 526 ....765 and then tested each one of them for possible continuation<o:p></o:p>

Not to big a task' - if someone does not err while going octal.<o:p></o:p>

My three possible answers:<o:p></o:p>

**3254167<o:p></o:p>**

**5234761<o:p></o:p>**

**5674321<o:p></o:p>**