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. 

Posted by Stephanie on 2009-03-30 16:52:35