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Fill 'er Up (The Full Reservoir in the UK version) is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

You are tasked with filling a reservoir by pumping water from a nearby lake using these four pumps.

If you filled the reservoir using only one pump at a time, pump A would take three days, pump B would take six days, pump C would take 10 days, and pump D would take 15 days.

You decide to get one extra pump to make life easier. Which pump should you buy another of in order to get the job done in exactly one day?

UK Version

You are tasked with filling a reservoir by pumping water from a nearby lake using four pumps.

If you filled the reservoir using only one pump at a time, pump A would take three days, pump B would take six days, pump C would take ten days and pump D would take 15 days.

You decide to get an extra pump to make life easier. Which pump should you buy another of in order to get the job done in exactly one day?

Hints




Click a Tab to reveal the Hint.

How much of the reservoir can each pump fill in one day?

Is there any convenient way to add these amounts together?

This puzzle can be solved by adding fractions together. If you dislike working with fractions, you can solve the problem by imagining the full reservoir has a certain amount of water in it.

US Version

Pump A can fill the reservoir in three days. Therefore, it fills a third of the reservoir in one day. Pump B takes six days, so it will fill a sixth in one day. Pumps C and D also follow the same logic. You should be able to work out what remaining fraction is required by adding them together.

UK Version

Pump A can fill the reservoir in three days. Therefore, it fills a third of the reservoir in one day. Pump B takes six days, so it will fill a sixth in one day. Pumps C and D also follow the same logic. You should be able to work out what the required remaining fraction is by adding them together.

US Version

Adding a third, a sixth, a tenth, and 1/15 gives exactly two thirds. Therefore, the reservoir requires a further third to be full. Which of the pumps is capable of providing that amount of water in one day?

UK Version

Adding a third, a sixth, a tenth and a fifteenth gives exactly two thirds. Therefore, the reservoir requires a further third to be full. Which of the pumps is capable of providing that amount of water in one day?


Solution

Incorrect

Too bad!

US Version

Try again.

UK Version

Don't be put off by the numbers.

Correct

Water good job!

With another pump A, the job would be done in exactly one day.

LS040S

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

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