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Fair Compensation is a puzzle in Professor Layton and the Diabolical Box.

Puzzle

US Version

Three houses face a single common field. The heads of these three houses, A, B, and C, decide to work together to seed the field. Unfortunately C injures himself right before work starts, so A and B do all the work together. To seed the entire field, A works five days and B works four.

Feeling guilty, C decides to pay A and B for doing his part of the job. To thank them, C pays them a total of nine coins, divided up according to how much work each person did. Can you figure out how many coins A and B received?

UK Version

Three houses face a single common field. The heads of these three houses, A, B and C, decide to work together to seed the field. Unfortunately, C injures himself just before work starts, so A and B do all the work together. To seed the entire field, A works five days and B works four.

Feeling guilty, C decides to pay A and B for doing his part of the job. To thank them, C pays them a total of nine coins, divided up according to how much work each person did. Can you work out how many coins A and B each received?

Hints




Click a Tab to reveal the Hint.

It's tempting to think that the answer is to pay each man a coin for each day he worked, resulting in a total of five coins for A and four coins for B. But then that wouldn't be much of a puzzle, would it?

Remember, the original agreement was that each man would do an equal share of the work.

Simply put, A and B are getting paid for doing the work C was supposed to do.

US Version

When considering your answer, don't factor in the days A and B were supposed to work according to the original agreement.

UK Version

When considering your answer, don't factor in the days A and B were supposed to work according to the original agreement. C wouldn't be paying them out of his own pocket for work they were supposed to do in the first place.

US Version

The coins should be distributed based on the number of days each person worked to cover the three days C was supposed to have worked.

A did two days, B did one.

UK Version

The coins should be distributed based on the number of days each person worked to cover the three days C was supposed to work.

A did two days, B did one.


Solution

Incorrect

Too bad!

When you think about it, the pay you suggested isn't quite fair.

Correct

Smart!

US Version

A received six coins and B got three. You might have been tempted to answer five and four coins respectively, but as shown above, that isn't quite correct, because A and B both had to work three days to finish their own shares of the work. Seeing how C wanted to pay A and B for the work they did for him, he had to base his payment on the two days of work A did and the only day of work B did. Therefore, A should receive twice the pay B did.

UK Version

A received six coins and B got three. You might have been tempted to answer five and four coins respectively but, as shown above, that isn't quite correct. A and B both had to work three days to finish their own shares of the work. Since C wanted to pay A and B for the work they did for him, he had to base his payment on the two days of extra work A did and the one day of work B did. Therefore, A should receive twice the pay B did.

DB114S

A big thanks to http://professorlayton2walkthrough.blogspot.com

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