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.

I'm haven't yet shown that this is the smallest positive integer that satisfies the problem, but my preliminary tests with a program I've written leads me to 1890 which can be written as a sum of consecutive positive integers in 14 different ways:

471-474
629-631
376-380
267-273
206-214
85-104
54-81
119-133
35-70
80-100
57-83
2-61
37-71
20-64

Posted by Thalamus on 2004-06-28 15:05:18