Discussion
The opposite sides of a solid cube of 8 ×8×8 cm is coloured with Red, Green and Yellow. After that cube is cut into 2 cm small and equal size cubes. Number of small cubes which have two sides coloured with Red and Yellow is :
Answer: D
The number of such cubes is 8.
Cutting an 8 cm cube into 2 cm cubes gives \(4 \times 4 \times 4 = 64\) small cubes, 4 along each edge. Each pair of opposite faces has one colour: two red faces, two green and two yellow.
A small cube with exactly two coloured faces lies on an edge of the big cube but not at a corner. The edges where a red face meets a yellow face number \(2 \times 2 = 4\), and each such edge has \(4 - 2 = 2\) non-corner cubes. So there are \(4 \times 2 = 8\) cubes coloured red and yellow.
16 counts all four cubes along each red-yellow edge, including the corner cubes, which have three coloured faces; 4 counts only one cube per edge, and 32 counts far more edges than meet red to yellow.
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