+0  
 
+1
40
1
avatar

A 2x2x2 cube is to be constructed using 4 white and 4 black unit cubes. Adjacent cubes should have different colors.  How many different cubes can be constructed in this way?

(Two cubes are not different if one can be obtained by rotating the other.)

 Feb 12, 2021
 #1
avatar+62 
+2

When you state that adjacent cubes have different colors, then the layers must be like this:

First layer:

w b
b w

Second Layer

b w
w b

 

If we inverse the colours, then we can rotate the new cube 90 degrees to get the original cube we first drew.

 

So there is only $\boxed{1}$ possible cube.

 Feb 12, 2021

25 Online Users

avatar
avatar