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 Roll a unit (Posted on 2019-11-06)
A cube with edge length 7 units is painted on all faces. It is then cut into 73 unit cubes. These cubes are put in a bag, one is chosen at random and rolled.

What is the probability the side that faces up is painted?

 Submitted by Jer Rating: 1.0000 (2 votes) Solution: (Hide) I'll give the general solution for a nxnxn cube. When painted 6n^2 unit squares will be painted. There are 6n^3 total sides. The chosing and rolling assures that each of these total sides has the same probability of being chosen. (6n^2)/(6n^3)=1/n. So the probability when n=7 is 1/7 -------------------------------------------------------------- Another very slick way of looking at this. Consider the top face of the big cube. Each little cube has paint on this side, but there are n-1 cubes below it that don't. The same holds in each direction so the answer is 1/n.

 Subject Author Date soln Steven Lord 2019-11-06 10:32:01 In-the-head solution (spoiler) Charlie 2019-11-06 10:31:12

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