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Dirt Patchwork is a puzzle in Professor Layton and the Unwound Future.

Puzzle

US Version

You found a nice, round patch of dirt that you'd like to divide up into as many different garden plots as possible.

You have five ropes to work with. Each one must be stretched in a straight line across the circle, but the ropes can cross each other as often as you like.

Using only these five ropes, what is the maximum number of sections you can divide the patch of dirt into?

UK Version

You found a nice circular patch of soil that you'd like to divide up into as many separate plots as possible.

You have five ropes to work with. Each one must be stretched in a straight line across the patch, and they can cross each other as often as you like.

Using only these five ropes, what is the maximum number of sections you can divide the patch of soil into?

Hints




Click a Tab to reveal the Hint.

The five ropes would simply create six sections if you weren't allowed to cross them.

But you're allowed to cross the ropes, so you can create a lot more spaces.

If you stretch a rope across the patch of dirt from top to bottom and another from left to right, they'll cross in the middle and divide and patch into four different sections. And that's using just two of your five ropes!

With your five ropes, you can divide the patch of dirt into more than 10 different sections.

Use the Memo function to draw a star in the middle of the circle using the five straight lines. Make sure the points of the star are within the circle and the lines creating each point cross and extend out into the grass so they create one more space within the circle.

Now count each section. Well, how many are there?


Solution

Incorrect

Too bad!

The sections can be all different sizes. The important thing is to divide the patch of dirt into the maximum number of spaces.

Correct

Excellent!

US Version

You can divide the patch of dirt into as many as 16 different sections!

The first rope divides the circle into two sections. The second rope divides it into four. The third rope crosses the first two and divides the patch into seven sections. Once you've used all five ropes like this, you end up with 16 sections!

A simple example is a star in the center as shown in the image above.

UK Version

You can divide the patch of soil into as many as 16 different sections!

The first rope divides the circular patch into two sections. The second rope divides it into four. The third rope crosses the first two and divides the patch into seven sections. Once you've used all five ropes like this, you end up with 16 sections!

In other words, you form a star in the centre of the patch, as above.

UF160S

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

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