Can you arrange the digits 1-9 in any order so that:

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

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

The number formed by the first four digits is divisible by 4

and so on up to nine digits...

It is obvious that
1) The even digits must go in the even positions

2) The 5 must go in the fifth position

3) The 2 and the 6 must be in positions 4 and 8 in some order

4) Dividing the number into three goups of three (Separating the number at the thousands and million commas) results in three numbers each divisble by three.

As I see it, the tough part will be finding the seven digit number divisble by seven. Once you know that, everything else falls into place.

Posted by TomM on 2002-06-06 05:35:54