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Settle the Scores is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

Three darts players have just finished a game. Based on the point totals shown, can you work out how many points each color section of the dartboard is worth?

No two sections have the same value, and their values increase the closer they are to the center. Each is worth a single-digit value of at least one point.

Hints




Click a Tab to reveal the Hint.

The middle player's dartboard has two darts each in section A and section D, for a total of 26 points. So sections A and D must add up to half of 26, or 13.

What does that mean?

The left player's dartboard has one dart in each section from A to D, for a total of 25 points.

From Hint 1, you know that A + D = 13, so subtracting that from the total tells you that B + C = 12.

The right player's dartboard has one dart in section B and three in section C. You already know that B + C = 12, so subtract that from from the total, and you have 10 points left for the other two darts in section C. That means section C is worth 5 points.

Now you just need to substitute that value in the other equations you've worked out using the previous hints.

The previous hints have shown that C = 5 and B + C = 12. Thus, B = 7.

The puzzle description tells you that A must be higher than B but still a single digit, so it has to be either 8 or 9.

D cannot equal 0, and must be lower than C, so it has to be 1, 2, 3, or 4. And you already know that A + D = 13...


Solution

Incorrect

Too bad.

One of the three players' results should be easier to analyze than the others.

Correct

Correct!

A = 9, B = 7, C = 5, and D = 4.

As long as you remember that the only possible values are from one to nine, this is just simple calculation.

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

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