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>

Posted by Ady TZIDON on 2009-03-30 17:09:09