Professor Layton and the Last Specter/Puzzles 126-156

Caution! This page contains all the hints and solutions for every puzzle from 126 to 156. Scroll carefully or you might spoil the answer of a puzzle for yourself. The solutions are hidden behind spoiler tags, so only take a peek if you're desperate.

Puzzle 149

 * Name: Marble Thirds
 * Trigger: Repeatedly tap shrubs
 * Location: Market East
 * Chapter: 4
 * Picarats: 30

Description: The diameter of the circle below is divided into three equal lengths, and those lengths are used to make the marble-like design that splits the circle into three different-colored sections.

The areas of sections I and III are equal, but what about the area of section II? Is it less than, greater than, or equal to the area of I?


 * Hint 1: Bear in mind the following three sizes of semicircle: The biggest semicircles in the diagram. The medium-sized semicircles, with a length two-thirds the circle's diameter. The smallest semicircles, with a length one-third the circle's diameter. Use these different-sized semicircles to help you solve the puzzle.
 * Hint 2: Think of the area of the smallest semicircle as one. The diameter of the medium semi-circle is twice that of the small semicircle, so its area will be four times as large. The big semicircle has a diameter three times as big as the small one, so the area will be nine times as large.
 * Hint 3: To figure out the area of sections I or III, use the semicircles as follows: Big - Medium + Small = . Replacing these with the areas we found in Hint 2 gives us: 9 - 4 + 1 = 6. This should help you figure out how to determine the area of section II.
 * Super Hint: If you've followed along with all of the previous hints, the rest is easy. The big semicircle has an area of nine. Since it's a semicircle, the area of the whole circle is twice that, or 18. From this, subtract the size of the areas of sections I and III, and you're left with the area of II. All right then. What is it?