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

Puzzle

"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 of 15 in. long. How far along the side should he cut?

Hints




Click a Tab to reveal the Hint.

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.

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.

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?

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?


Solution

Correct

Correct!

"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!"

LS064S

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