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Ball-Dart Bull's-Eye (Ball Dart Bullseye in the UK version) is a puzzle in Professor Layton and the Miracle Mask.

Puzzle

A, B, and C are playing a game of ball darts. After throwing four balls each, all three people scored 62 points.

A scored 27 points with his first two balls, and B scored five points with her last ball. The picture above shows where each ball hit the target.

Who threw the ball that hit the bull's-eye and scored 50 points?

Hints




Click a Tab to reveal the Hint.

First, you'll need to work out the combination of points needed for the three balls that didn't hit 50.

There should be four possible patterns.

Given that someone scored a 50, there are four possible combinations that can get them up to 62 points:

1. 50, 6, 5, 1
2. 50, 6, 4, 2
3. 50, 5, 4, 3
4. 50, 5, 5, 2

Using these as a reference, can you determine who scored the 50?

Think about A's score. He scored 27 with his first two balls, so that means he must have scored a 25 and a 2. That leaves 35 points, so he can only have scored a 30 and a 5 after that. That rules out A.

Following on from Hint 3, we now know that A's combination was 30, 25, 5, 2.

Observe the four patterns in Hint 2 again. We can rule out patterns 2 and 4 because we know that A scored the only 2. Which leaves the following:
1. 50, 6, 5, 1
3. 50, 5, 4, 3

Didn't B score a 5 with her last ball?


Solution

Incorrect

Too bad.

Use what you know to narrow down which balls could belong to each player.

Correct

Correct!

We know that A had to have scored a 30, a 25, a 5, and a 2. Additionally, by looking at all possible three-ball, 12-point combinations that take the score from 50 to 62, and by excluding A's 2 from these combinations, the one who hit the bull's eye must have scored a 5.

Two balls hit the 5-point area, one of which was A's so only B could have got the 50-point score.

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

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