CV117 - Painting a Cube

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Painting a Cube
117T.gif
117B.gif
Puzzle Number 117
Puzzle Name Painting a Cube
Picarats Given 30 Picarats
Type Write Answer
Location Tower Road
Previous Puzzle CV116 - The Largest Total
Next Puzzle CV118 - Red and Black Cards

This is the one hundred and seventeenth puzzle that appears in Professor Layton and the Curious Village. To access this puzzle, you must examine the rightmost window. In order to solve this puzzle, you must determine how many different ways the cube can be painted so that all faces that touch are different colors.

Contents

[edit] Hints

Hint One
    As you know, all cubes have six sides. Because of this structure, every face of the cube touches four others, meaning that only one of the five other faces doesn't touch any given face.

Hint Two
    Taking Hint One a step further, in order to paint the cube three colors and have no two connecting faces be of the same color, you should use each color to paint opposing faces.

Hint Three
    You need to paint two opposing faces of the cube each color. Count how many different ways there are of doing that and you've solved the puzzle.

    Just remember, simply reconfiguring which colors go where doesn't count as an entirely new arrangement.


[edit] Messages

[edit] When Failed

Nope!

All rotated or color-swapped versions of a particular painting scheme count as the same pattern. Don't count them as separate patterns when tallying up the total number of possible solutions.

[edit] When Completed

If you have to paint the cube with three colors, then your only choice is to paint opposing sides of the cube the same color.

As seen in the diagram above, even if you were to change where you used each color, rotating the cube proves that you're really just reusing the same idea of painting opposing sides the same color.

There's only one unique way to color this cube using three paints.

[edit] Solution

117ST.gif

The cube can be painted only one way.

[edit] Progress

2815 Picarats and 138 Hint Coins.



Last edited by Squiggle on 6 January 2016 at 03:18
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