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Mopping Up is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

These poor-quality mops take two days to dry after they've been used, and the handle completely breaks after just three uses!

What is the minimum number of mops that you would need to clean every day for a 30-day month?

UK Version

The quality of these mops is so poor, they take two days to dry after the day they were used. And they break after just three uses.

What is the minimum number of mops that you would need to clean every day for a month of 30 days?

Hints




Click a Tab to reveal the Hint.

Think about how many mops should be necessary for 30 days. Then see if there is any way you can reduce that number.

Each mop has to dry for two days, so you will need three mops for the first three days. It will take nine days until these mops are broken. Try to apply this pattern to the whole month.

If three mops are used over nine days, then nine mops are used to clean for 27 days.

How many mops are needed for the remaining three days? Try to think about the smallest number needed.

The key is in thinking about how you divide up the remaining three days. If you leave it until the end of the month, you will need three mops, but what would happen if you spread these days out throughout the month?


Solution

Incorrect

Too bad!

US Version

Try to be as economic with your mops as possible.

UK Version

Make sure you think economically and don't waste any mops.

Correct

You mopped this puzzle up!

US Version

You would need 10 mops. The trick is to use your fourth mop frugally! Three mops are used up every nine days. The fourth mop can be used once on the 10th day. Follow the same pattern for the next 10 days, using the fourth mop again once. By the 30th day, you will have used only 10 mops.

UK Version

You would need ten mops. The trick is to use your fourth mop frugally! Three mops are used up every nine days. The fourth mop can be used once on the 10th day. Follow the same pattern for the next ten days, using the fourth mop again once. By the 30th day, you will have used only ten mops.
There are a few other mop distributions that work. Perhaps you found one of these alternative solutions.

LS007S

A big thanks to http://professorlayton4walkthrough.blogspot.com