LS031 - Light Height

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Light Height
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Light Height
Puzzle Number 031
Puzzle Name Light Height
Picarats Given 50 Picarats
Type Input
Location Closed Factory
Previous Puzzle LS030 - Book Stacks
Next Puzzle LS032 - Fit for a King

This is the thirty first puzzle in Professor Layton and the Last Specter. To access this puzzle, you must talk to Sebastian. In order to solve this puzzle, you must figure out the height of the light.


[edit] Hints

Hint One
    Choose one of the posts, and visualize a large triangle formed between the light, the spot on the floor directly under the light, and the farthest point of the post's shadow. then imagine a smaller triangle formed between the top of the post, the bottom of the post, and the tip of the shadow.

    These two triangles are mathematically similar. In other words, the larger one is proportional to the smaller one.

Hint Two
    Let's say that the height of the light equals X, and the distance on the floor between the light and the post on the left equals Y.

    The shadow cast by the post on the left extends 3 feet.

    X:(Y:3)=1:3, therefore

Hint Three
    The shadow of the post on the right is 2 feet long.

    X:(15-Y+2)=1:2, therefore

Super Hint
    By combining the solutions from the equations of Hint 2 and Hint 3, you get:

    5X=20, therefore

    The height from the light to the floor equals X.

[edit] Messages

[edit] When Failed

Too bad!

Your calculations aren't quite correct.

[edit] When Completed

That's right! The light is 4 feet tall!

As shown in the diagram, make two triangles, ABC and EBF, on the left of the light and two more, ADC and GDH, on the right.

AC:BC = EF:BF therefore
X:(Y + 3) = 1:3
AC:CD = GH:HD therefore
X:(15 - Y + 2) = 1:2

Solving both of these equations will give you the value of X.

[edit] Solution

The light is 4 feet tall.

[edit] Progress

1115 Picarats and 120 Hint Coins.

Last edited by Squiggle on 8 September 2015 at 21:13
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