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I have a unit cube and $6$ colors to paint its sides in. How many different cubes to I get if I use one color per side?

I think I know the answer, but just want to be sure regarding my solution. Let colors be numbers $1,2,\dots,6$ and let us fix a side where we put $1$. We have $5$ options for the opposite side. So we are left with a cyclic 4 sides and 4 numbers to put on them: let us now call them $a,b,c,d$. We fix a side where we put $a$ and we are left with $3!$ options for other sides. As a result the answer is $5\cdot 3! = 30$.

vonbrand
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S.D.
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1 Answers1

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You are on the right track.The answer is right since the symmetry of cube makes the cases you have advanced for

dsinghvi
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