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Consecutive Integer Sums (Posted on 2004-06-28) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 4.3333 (3 votes)

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re(2): Computer solution | Comment 15 of 22 |
(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 2004-06-29 08:07:06
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