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Cutting the Cake is a puzzle in Professor Layton and the Last Specter.

Puzzle

US Version

"I suppose I could share this triangular cake. It's really tasty, but I can spare half of it, and my friends can divide that between them.

Then again, it is my cake. It's only fair that I should have most of it...

I'll just cut two pieces with a ratio of 4:5 and take the bigger piece. That's still pretty generous, isn't it?"

The sides of the cake are 15 in. long. How far along the side should he cut?

UK Version

"I suppose I could share this triangular cake. It's really tasty, but I can spare half of it, and my friends can divide that between them.

Ngh, but it is my cake. It's only fair that I should have most of it...

I'll just cut two pieces with a ratio of 4:5 and take the bigger piece. That's still pretty generous, isn't it?"

The sides of the cake are 15 cm long. How far along the side should he cut?

Hints




Click a Tab to reveal the Hint.

US Version

You don't need to perform complicated math calculations to solve the puzzle.

You just need to remember that with this equilateral triangle, each side is the exact same length: 15 in.

UK Version

You don't need to perform complicated calculations to solve this puzzle.

The key to the puzzle is that the cake is an equilateral triangle with sides 15 cm long.

US Version

Is it possible to divide the cake into several smaller equilateral triangles?

If you can figure out a way to do that, it should be easier to determine the correct proportions of the two final slices.

UK Version

You could cut this cake into several equal-sized mini pieces.

What would the length of one of these mini pieces be?

US Version

To divide the cake into portions with a ratio of 4:5, you could cut the top section into four tiny pieces of the same size.

Therefore, how long would the side of these tiny pieces be?

UK Version

To divide the cake into portions with a ratio of 4:5, you could cut the top section into four mini pieces and the bottom into five mini pieces of the same size.

Therefore, how long would the side of one of these mini pieces be?

US Version

Try dividing the cake into triangular pieces with 5 in. sides.

You should end up with nine pieces of cake. Can you see where you need to cut the cake now?

UK Version

Try dividing the cake into triangular pieces with 5 cm sides.

You should end up with nine pieces of cake. Can you see where you need to cut the cake now?


Solution

Incorrect

US Version

Too bad!

Keep in mind that the cake is in the shape of an equilateral triangle.

UK Version

Crumbs!

You shouldn't have to think too hard. Just remember that the cake is an equilateral triangle.

Correct

Correct!

US Version

"I can have my cake and eat it, too!

If I cut the side at 10 in. as shown, the proportion of the portions is exactly 4:5.

I can eat lots of cake and share with my friends, too!"

UK Version

"I can have my cake and eat it!

If I cut the side at 10 cm as shown, the proportion of the portions is exactly 4:5.

I can eat lots of cake and share with my friends, too!"

LS064S

A big thanks to http://professorlayton4walkthrough.blogspot.com

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