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Eight sets of scales, sixty-four coins, huh? Oh, there's one missing? On balance, I'm sure you can make everything add up. Also consider the total weights for each set of scales.

Making scales balance with four coins stacked on each side totally isn't as hard as you might think. On scales, the heaviest weight goes on the bottom.

There's only one way to balance a coin with a "5" at the end: put three coins that end with a "1" and one that ends with a "2" on the other side. Then stack the coins by weight and compare each side. Notice any similarities?