Puzzle | Six colored cube

Given six distinct colors, in how many unique ways can a six faced cube be painted such that no two faces have the same color?
Note: Mixing of colors is not allowed.

Answer: 30 ways

To avoid repetitions, let us fix the color of the top face.
Hence, the bottom face can be painted in 5 ways.
Now, what remains is the circular arrangement of the remaining four colors which can be done in (4-1)! = 3! = 6 ways (For n distinct objects, number of distinct circular arrangements are (n-1)!).
Hence, the answer is 5*6 = 30 ways.

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.