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## Triangle Numbers

Series teasers are where you try to complete the sequence of a series of letters, numbers or objects.

 Puzzle ID: #14508 Fun: (2.73) Difficulty: (2.89) Category: Series Submitted By: Smithy

Triangle numbers are formed by adding successive integers, i.e.

1 = 1+0,
3 = 1+2,
6 = 1+2+3,
10 = 1+2+3+4,
etc.

So the first few triangle numbers would be:

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

Suppose somebody tells you a random integer. How can you quickly find out whether or not it is a triangle number?

Multiply the number by 8 then add 1. If the result is a perfect square, then the original number is a triangle number.
For example: 10*8+1 = 81. 81 = 9^2. So 10 is a triangle number.
11*8+1 = 89. 89 is not a perfect square, so 11 is not a triangle number.

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