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What are the Triangle numbers up to 21?

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What are triangle numbers?

Triangle numbers are a series of sums of the first n numbers. Thus T1 = 1 T2 = 1+2 = 3 T3 = 1+2+3 = 6 T4 = 1+2+3+4 = 10 However, rather than ading up a whole lot of numbers,

How can numbers 1-9 add up to 15 on each side of the triangle?

The numbers 1-9 sum to 45. If they are to be sum to 15 on each of three sides of a triangle, no number can be counted more than once (15*3 = 45). That is, there are no numbe