perplexus.info :: Sequences : Triangle Numbers

Triangle Numbers (Posted on 2003-08-07)

Triangle numbers are :

1,3,6,10,15,21,28.

Somebody tells you a random positive integer of any size. Is there a quick way to work out if it is a triangle number or not (in other words, without going through all of the triangle numbers untill you get to a number as high or higher as the integer you've been told)?

Submitted by Lewis

Rating: 3.0000 (6 votes)

Solution: (Hide)

Call the random positive integer that you were told X.
To work out if X is a triangle number, you do the sum (x*8)+1. If the result is a square number, then X is a triangle number.
For example, 6*8 is 48. Add 1 to get 49. Because 49 is a perfect square (49 = 7^2) then 6 is a triangle number.
8*8 is 64. Add 1 to get 65. Because 65 is not a perfect square then 8 is not a triangle number.
Also, when you have done (x*8)+1, if it does equal a square it will equal the square of an odd number.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution: Method II	K Sengupta	2008-05-08 14:26:03
Puzzle Solution: Method I	K Sengupta	2008-05-08 14:24:36
Quadratic	Adam Sisco	2003-08-11 02:40:29
Simpler Derivation	DJ	2003-08-07 21:25:56
No Subject	LynetteVivian	2003-08-07 20:36:17
Another simple method	Gamer	2003-08-07 18:32:32
No Subject	LynetteVivian	2003-08-07 17:53:57
re: Simple Method	Brian Wainscott	2003-08-07 16:48:37
Simple Method	DJ	2003-08-07 15:27:26

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