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.

945 has at least twelve ways to be formed as a sum of two or more consecutive positive integers. 12 starting values are 472, 314, 187, 155, 132, 101, 90, 61, 56, 44, 35, and 22 with 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, and 27 terms resp.

I think the analytical (no computer program) difficulty level of this problem is higher than 3. However, somebody should be able to settle this with a computer program of difficulty level 3 or lower.

Edited on June 28, 2004, 6:43 pm

Posted by Richard on 2004-06-28 18:28:05