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.

Please note that I have edited the previous comment to include a fuller discussion of Riley's simple method for this problem.

Edited on July 4, 2004, 8:55 pm

Posted by Richard on 2004-07-03 15:32:30