Pool Ball Neighborhoods

Fifteen pool balls (numbered 1 through 15) are packed in the standard rack, labeled A through P in the upper diagram at left. The neighborhood sums and row sums of each ball are given in the lower diagram. For example, 60 is the sum of the seven balls around E (including B, C, D, E, F, H, and I), and 35 is the sum of the row of balls beginning with G.

If the 8-ball is in position J, where are all the other balls?

(solution)

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