Est. 1998 — 27 years of woodworking knowledge
Friday Puzzler -- painted cubes
Alex Y
You are given an unlimited supply of wooden cubes and six cans of paint, with different colors. You are to paint cubes with one color on each face, using all six colors on each.
How many distinctly-colored cubes can you create. Two cubes are distinctly colored if there is no way to rotate them so that each pair of corresponding faces is the same color.
Re: Friday Puzzler -- painted cubes
Sam Force
With 6 cans of paint the number of "colors" are as endless as the cubes. You did not say that they could not be mixed
No mixing
Alex Y
But you are correct. I did not make that restriction clear.
What is your answer if each cube must be painted with one face each of red, yellow, blue, orange, green, and purple?
Re: No mixing
Sam Force
I do not think the number is high, but not positive. 21 comes to mind but I'm not a mathematician
Sorry, but not 21
Re: Friday Puzzler -- painted cubes
JohnV
5!/2
Sorry, but not 60
Re: Friday Puzzler -- painted cubes
Larry Barrett
Rotations clearly limit the possible variations and trying to picture these rotations is difficult.
Choose one face and call this the top; call the opposite face the bottom.
Put any color on the top and put any of the remaining 5 on the opposite face (5 variations).
Next put any of the remaining 4 colors on one of the adjacent faces and put any of the remaining 3 colors on the opposite face (3 variations).
The remaining 2 colors can now go on either of the remaining 2 faces (2 variations).
So 5x3x2 = 30 possible variations.
Correct!
Alex Y
And I find that envisioning of physically counting the possibilities much easier than trying to work with combinations or permutations.