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You're in a shop that has a special bottle-return policy: you can get one full bottle of juice for every three empty bottles you bring in. A customer comes and buys five dozen and seven bottles of juice.
How many bottles of juice will the customer ultimately get to drink if he keeps returning empties?
Are you forgetting to count any bottles?
Correct--100 bottles of juice in all!
He'd get 22 full bottles from his first 67 empties, with one empty bottle left over. Next, he'd get seven full bottles for the with another bottle left over. After that, he'd get three full bottles for the nine empty ones he'd have by that point. Finally, he can get one last full bottle from the last three empties.
The shopkeeper might want to rethink his policy...
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