The integer 30 can be written as a sum of consecutive positive integers in three ways:
30 = 9+10+11 = 6+7+8+9 = 4+5+6+7+8.

Find the smallest positive integer which can be written as a sum of consecutive positive integers in 12 ways.

(In reply to Possible Solution by Richard)

I was just going through the possibilities, and I refreshed my page as I came accross 945.  I guess I'm a little late, but...

945 has 14 ways to be written as a sum of consecutive integers.  The lengths are:

2,3,5,6,7,9,10,14,15,18,21,27,30,42

Dividing 945 by the length of the sequence will result in the middle number or the average of the two middle numbers.

I believe this is the lowest possible number, but I can't prove it.

Posted by Tristan on 2004-06-28 18:38:17