Question

A cube is painted so that one side is blue, two sides are red, and three sides are green. How many different such cubes can be painted? Two cubes are considered the same if one cube can be rotated in any way to match the second cube.

Answer 1

So there are 3 distinct cubes.

Explanation:

There are total six sides of the cube.

if we observe the given data and fix the sides of the cube by the color

So,

let suppose,

Blue color is painted on the top side of the cube

Now, we have left 5 sides

as per the information 2 sides are painted by Red color

let suppose,

1 Red color is painted on bottom side And 1 is on side

Now, we have left 3 sides

And 3 sides are green as per the given information.

1 green color painted on the adjacent side of the red side

1 green side is opposite of red side.

and 1 opposite of green side.

Now all side are colored and if we observe the above scenario

All other possibilities can be rotated to one of these.

So there are 3 distinct cubes.