Question:medium

A cuboid-shaped wooden block has dimensions 6 cm \(\times\) 4 cm \(\times\) 1 cm.
\(\bullet\) The two 4 cm \(\times\) 1 cm faces are coloured black.
\(\bullet\) The two 6 cm \(\times\) 1 cm faces are coloured red.
\(\bullet\) The two 6 cm \(\times\) 4 cm faces are coloured green.
The block is cut into small cubes of side 1 cm.
Question: How many cubes having red, green, and black colours on at least one side of the cube will be formed?

Show Hint

For a single-layer cuboid (\(L \times W \times 1\)), the cubes with 3 colors are always the 4 corner cubes. No other cubes can touch the "end" (Black) and "side" (Red) faces simultaneously.
Updated On: Jun 30, 2026
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Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Map each face to its colour.
The 6x4x1 cuboid is cut into $6 \times 4 \times 1 = 24$ unit cubes in a single flat layer; the two 4x1 end faces are Black; the two 6x1 long side faces are White; the two 6x4 top and bottom faces are Red.
Step 2: Determine which cubes touch Red.
Since the cuboid is only 1 cm thick, every unit cube spans the full height and therefore touches both the top and bottom Red faces - all 24 cubes contact Red.
Step 3: Find cubes touching all three colours.
Cubes touching Black are at the two short ends; cubes touching White are at the two long sides; a cube touching both Black and White must sit at a corner where an end meets a side - in the 6x4 grid there are exactly 4 such corner positions, each also touching Red, so exactly 4 cubes touch all three colours.
\[ \boxed{4} \]
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