LS149 - Marble Thirds

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Marble Thirds
PL4149B.png
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Puzzle Number 149
Puzzle Name (US)Marble Thirds
(UK)Marble Swirl Circle
Picarats Given 30 Picarats
Type Button
Location Market East
Previous Puzzle LS148 - Glass Boxes
Next Puzzle LS150 - Lily Pad Leapfrog

This is the one hundred and forty ninth puzzle in Professor Layton and the Last Specter. To access this puzzle, you must examine the plant above Socket. In order to solve this puzzle, you must figure out if the area of section II is less, greater or equal to the area of section I.

Contents

[edit] Hints

Hint One
    Bear in mind the following three sizes of semicircle:
    • The biggest semicircles in the diagram.
    • The medium-sized semicircles, which 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 Two
    Think of the area of the smallest semicircle as one. The diameter of the medium semicircle 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 its area will be nine times as large.

Hint Three
    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're 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?


[edit] Messages

[edit] When Failed

Too bad!

There's a simple way to solve this puzzle. See if you can figure it out.

[edit] When Completed

Precisely!

The areas of I and II are the same! The best way to think about it is to use the three sizes of semicircles as shown above. If the ratio of the diameters is 3:2:1, then the ratio of the areas is 9:4:1.

Using the ratios as a guide, we can compare the areas of I, II, and III and conclude that they are, in fact, equal.

[edit] Solution

The areas are equal.

[edit] Progress

1280 Picarats and 135 Hint Coins.



Last edited by Squiggle today at 05:06
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