Triangle with equal side sums

HardCombinatorics Brainteasers~9m

The integers $1$ – $9$ are placed on the $3$ corners and $6$ edge-positions of a triangle (each side of the triangle holds $2$ corners and $2$ edge numbers; corners count toward both of their sides). If every side's four numbers sum to $17$ , how many distinct arrangements are there, counting rotations as the same and ignoring the order of numbers within a side?

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Summing all three sides double-counts corners: $3\cdot17 = 45 + \text{cornersum}$ , so corners sum to $6$ (i.e. $\{1,2,3\}$ ).
Enumerate edge fills to $17$ , then divide out the $3$ rotations.

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Asked at: Jane Street, Citadel

Triangle with equal side sums

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