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Free Lunch! is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

Every day, colleagues A, B and C spin a wheel to determine who will pay for lunch. The wheel is divided into 3 segments, worth the number of points indicated in the picture, and the colleagues spin the wheel six times. Each time, all three of them receive points according to which segment lands on them. Whoever has the fewest total points at the end has to pick up the bill.

Today, A has ended up with 13 points. If no two people finished with the same score, who had to pay for lunch?

Hints




Click a Tab to reveal the Hint.

The only score you know is A's: 13 points. To get this many points after six spins of the wheel, she could have got two points on five occasions and three points once, for example. What other combinations of points would give A a score of 13?

There are only three ways for A to have received 13 after six spins. Now you can look at the wheel and work out how many points B and C would receive.

When A gets 1, B get's 3. When A get's 2, B gets 1. When A gets 3, B gets 2. C gets the remaining points in each case. Oh, and don't forget that no two people got the same number of points, so you can rule out any combination that gives B or C the same score of 13 that A has.

There are three ways for A to receive 13 points, and you can exclude any case in which B or C also gets 13 points. There's only one way left, and that leaves A with 13 points, B with 7, and C with 16. The one with the fewest points pays for lunch.


Solution

Incorrect

Too bad.

You should be able to work out everyone's scores based on A's.

Correct

Correct!

B lost out and had to pay for everyone.

Spin, spin, spin! Don't you find yourself wanting to spin the lazy Susan when you get one at the restaurant?

A big thanks to http://www.youtube.com/user/LaytonKyouju

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