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
re: Computer solution by Richard)
The program did not find that there is no number that has exactly 12 nontrivial representations as the sum of consecutive positive integers. That's for two reasons:
1. As soon as it found one with 15 such representations, it considered only those subsequent numbers with more than 15. Any larger number that had exactly 12 representations would be lost.
2. It did not go high enough; it stopped searching at 30,000.
Now, having read subsequent discussion and gone to the recommended web site, I see we just need a number with exactly 12 odd factors. That's easy: 3^12 = 531,441. Setting my program on that number, the program comes up (in the same format as before) with:
177146 177148 177147
59045 59053 59049
19670 19696 19683
6521 6601 6561
2066 2308 2187
365 1093 729
265720 265721 265720.5
88571 88576 88573.5
29516 29533 29524.5
9815 9868 9841.5
3200 3361 3280.5
851 1336 1093.5
531441 12


Posted by Charlie
on 20040629 08:07:06 