Cube Puzzle
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You have a normal six sided cube. I give you six different colors that you can paint each side of the cube with (one color to each side). How many different cubes can you make?Different means that the cubes can not be rotated so that they look the same. This is important! If you give me two cubes and i can rotate them so that they appear identical in color, they are the same cube.
Answer: 30
Explanation: Choose a color and paint the bottom side, so now we can choose one of 5 color for the top side
Now, what remains is the circular arrangement of the remaining 4 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 3!*5 = 1*2*3*5 = 30 ways.
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