Juicy Returns is a weekly puzzle in Professor Layton and the Last Specter.


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?


Click a Tab to reveal the Hint.

Let's start by putting this in simpler terms. Buying five dozen and seven bottles gives you 67 full bottles. Returning all 67 bottles later gives you one full bottle for every three empties. That's 67 divided by three, or 22 bottles with one empty remainder. Keep repeating this calculation with the empties to work out how many bottles the customer gets to drink.



Too bad!

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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