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Puzzle - Hint

Below is a very special grid, around each shaded number are 8 white squares. However, each white square should have a number from 1 to 7. Once filled in, these 8 numbers will sum to the shaded number. In addition, once completed correctly, no row nor column will contain a duplicate number within a white square. For example, the top row may be 5 6 4 2 3 1 7, etc. This is a very difficult puzzle, and many people resort to using a computer to help them, which is a challenge in itself.

?

 [Ref: ZIWB] © Kevin Stone

Hint: This puzzle almost certainly requires trial-and-error to solve.

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