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Black and White Balls is a weekly puzzle in Professor Layton and the Unwound Future.

PuzzleEdit

There is a square that's completely filled with black and white balls. As you can see, however, only two corners of the square are visible. The rest of the square is not to scale and all the balls are not shown.

The outer edge all the way around is only black balls--36 in total. The rest are white, and there are no empty spaces.

So, how many white balls are there? The image below is just for illustrative purposes, so don't rely on it to solve the puzzle.

HintsEdit




Click a Tab to reveal the Hint.

You might think that since there are 36 black balls around the outside edge that each side of the square is made up of 9 black balls. However, this isn't true.


The corner balls are each shared by two sides, which means that each side is actually made up of 10 black balls.


Apply this information to the diagram, and you'll have the answer in no time.


SolutionEdit

IncorrectEdit

Too bad!

There are 36 black balls around the outside edge, so each side must be composed of nine black balls...right?

Actually, that's not right. Think carefully about it, and try again.

CorrectEdit

On the ball!

There are 64 white balls inside the square. The 36 black balls forming the outer edge mean that each row, both vertically and horizontally, is 10 balls long.

The total number of balls in the square, then, is 10 x 10 = 100. Subtract 36 black balls from the 100 total balls, and you have the total number of white balls: 100 - 36 = 64!

UFW33S

A big thanks to http://professorlayton3walkthrough.blogspot.com

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