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I have 4 blacks and 4 white cubes of equal size. In how many differe nt ways can they be put together to form a 2x2x2 cube?(Two cubes are not considered different if they can be rotated to look the same) -10marks

I have 4 blacks and 4 white cubes of equal size. In how many different ways can they be put together to form a 2x2x2 cube?(Two cubes are not considered different if they can be rotated to look the same) -10marks

Grade:12th Pass

2 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
7 years ago
There will be two layers of cube each containing 4 cubes.

Situation 1: If the upper layer has 4 black cubes the lower layer will have 4 white cubes.
Situation 2: If the upper layer has 3 black and 1 white cubes the lower layer will have 3 white and 1 black cubes.
Situation 3: If the upper layer has 2 black and 2 white cubes the lower layer will have 2 white and 2 black cubes.
There is no more other situatuons as the opposite side will resemble the above situation. Thus, there are 3 ways
You need not worry about the configuration of the side faces as either one of the face will resemble the original configuration when changed in any way.
TEJKIRAT SINGH
65 Points
6 years ago
here will be two layers of cube each containing 4 cubes. 
Situation 1: If the upper layer has 4 black cubes the lower layer will have 4 white cubes. 
Situation 2: If the upper layer has 3 black and 1 white cubes the lower layer will have 3 white and 1 black cubes. 
Situation 3: If the upper layer has 2 black and 2 white cubes the lower layer will have 2 white and 2 black cubes. 
There is no more other situatuons as the opposite side will resemble the above situation. Thus, there are 3 ways 
You need not worry about the configuration of the side faces as either one of the face will resemble the original configuration when changed in any way.

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