Lesson 2 of 4 · Painted cube cut into smaller cubes
Colour pattern
Cubes and Dice · for IPMAT Indore, IPMAT Rohtak and JIPMAT · asked in JIPMAT 2021
The exam method
- Colour edges. Opposite faces in pairs (red, blue, green): a red–blue edge exists for each red face and each blue face: 2 × 2 = 4 edges, n − 2 cubes each.
Worked examples
Example 3Easy
A cube is painted green on top, yellow at the bottom and red on the four sides, then cut into 216 cubes. How many have exactly two painted faces of different colours?
Solution: 32. n = 6. The 4 vertical edges join red to red; the 4 top edges (green–red) and 4 bottom edges (yellow–red) qualify: 8 × (6 − 2) = 32.
Example 1Sitter
A cube painted on all faces is cut into 125 equal cubes. How many have no painted face?
Solution: n = 5; (5 − 2)³ = 27.
Formulas you need
Watch out
- Same-colour edges: in "two faces of different colours", edges where two faces of one colour meet do not count.
Picked from the Painted cube cut into smaller cubes note for this micro-concept automatically. The whole note: Painted cube cut into smaller cubes.