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You can't just add the balances and expect it to amount to the same as the spend. Consider this: you spend 0, 0, 0, 50. Your balances are 50, 50, 50, 0. Adding up the balances you get 150. What does this mean? Absolutely nothing.
Maybe 1, 1, 1 -> 49, 48, 47 is a better example though. But same thing.
I wanted to keep it simple and avoid a factorial sum. My example also shows that the remainder sum goes up even when nothing is spent.
“I am your father’s brother’s nephew’s cousin’s former roommate”
"What's that make us?"
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