|←||116 - The Largest Total||117 - Painting a Cube||118 - Red and Black Cards||→|
In front of you sits a blank paper cube that you've decided to paint. You need to paint the cube so that all faces that touch are different colors.
Using three colors of paint, how many ways can you paint the cube so that it satisfies the above condition?
Each painting scheme should be a different pattern, not just the same pattern with the colors rearranged. Also, assume that you can't leave any sides of the square blank.
All rotated and 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.
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.
|Professor Layton and the Curious VillagePuzzles in|
See here for weekly puzzles
|Puzzle Index: CV · DB · UF · LS · MM · AL · VS|
A big thanks to http://professorlaytonwalkthrough.blogspot.com