A cube whose two adjacent faces are coloured, is cut into 64 identical small cubes. How many of these small cubes are not coloured at all?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 36
64 identical cubes come from cutting the big cube into \(4\times4\times4\), so each face of the big cube has \(4\times4=16\) small cubes. The two coloured faces are adjacent, so they share one edge of 4 small cubes, which must be counted only once.
Coloured cubes: \(16+16-4=28\)
Not coloured at all: \(64-28=36\)
Shortcut: Cutting away one coloured face layer leaves \(4\times4\times3\); cutting away the other leaves \(4\times3\times3=36\) cubes with no colour.