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Digits 1-7 (Posted on 2009-03-30) Difficulty: 2 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re: computer solution | Comment 3 of 6 |
(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
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