This question is based on the information given below: The six faces of cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue and green. The cube is then cut into 36 smaller cubes in a manner that 32 cubes are of one size and the rest of a bigger size and each of the bigger cube has no red side. How many cubes only have one side coloured?
This question is based on the information given below: The six faces of cube are painted in a manner that no two adjacent faces have the same colour. The three colours used in painting are red, blue and green. The cube is then cut into 36 smaller cubes in a manner that 32 cubes are of one size and the rest of a bigger size and each of the bigger cube has no red side. How many cubes only have one side coloured?
Solution
Given information:
Total cubes after cutting
cubes of one size, cubes bigger
Six faces painted with red, blue, green
No adjacent faces have same color
Bigger cubes have no red side
To find cubes with exactly one colored side:
From standard cube layout:
Corner pieces () have three colors
Edge pieces () have two colors
Center pieces () have one color
Inner pieces () have no color
When cut into pieces:
Must be a cube with an extra layer making it pieces
smaller cubes and bigger ones
To find cubes with only one side:
Center pieces would have only one color =
Edge middle pieces in extended layer = more
Total =
Therefore, cubes have exactly one colored face.