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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 numbers at any of the vertices.

Then there are several possible options:

1, 5, 9 along one side,

2, 6, 7 along the second

3, 4, 8 along the third.

So, if x marks the vertices

. . . . .x

. . . .1 . 2

. . .5 . . . 6

. . 9 . . . . . 7

. x . 3 4 8 . x

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