Question

A cube is painted red on two adjacent faces and on one opposite face, pink on 2 opposite faces, yellow on two opposite faces. Now the cube is cut into 125 equal sized small cubes. How many sides have all three colours?
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Answer 1

Answer:

Step-by-step explanation:

Because the cube is painted red on 2 adjacent faces, it will be painted yellow on the two opposite adjacent faces, making an “L” shape of yellow. If any cube is cut into 125 equal cubes, each face will be cut 5 times one way, and 5 times perpendicular to the first cut, making 25 cubes for each face. (5 x 5 x 5 = 125)

Each yellow face will therefore be cut into 25 cubes, but the line of 5 cubes where the two yellow faces meet at the base of the “L” will have 2 faces painted yellow, which eliminates 10 yellow faces so there will be

25 + 25 - 10 = 40 cubes with only one face painted yellow.

Hope this helps