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 More Triangle Numbers (Posted on 2004-01-15)
Triangle numbers are calculated taking each integer plus all the ones before it. The first triangle number is 1, the second is 1+2 or 3, and the third is 1+2+3 or 6.

If you take 8 times a triangle number plus 1, the result will be a perfect square. This number also will be the square of the triangle number's place doubled, plus one.

For example, 6 is third in the triangle number sequence. (1, 3, 6...) This means 8 times 6 plus 1 = 49 equals 3 times 2 plus 1, squared, or 7 squared.

Prove why this works.

 See The Solution Submitted by Gamer Rating: 3.0000 (4 votes)

 Subject Author Date Puzzle Solution K Sengupta 2008-11-14 06:03:19 No Subject SRay 2005-03-22 16:13:38 Geometric Solution nikki 2005-01-27 21:23:40 Solution Larry 2004-01-28 20:18:12 arithmaticely bharath 2004-01-15 13:29:10 Geometrically e.g. 2004-01-15 10:13:08 Solution Penny 2004-01-15 09:34:21 Solution retiarius 2004-01-15 09:04:28

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