TIFR CSE 2023 | Part B | Question: 13

Question

You have a regular tetrahedron and $4$ distinct colours. You wish to paint the faces of the tetrahedron such that each face gets a different colour. How many ways can you colour the tetrahedron? Recall that a regular tetrahedron is a three-dimensional solid with exactly four faces, all of which are equilateral triangles: see the sketch given below (not drawn to scale) for a rough view of such a solid. Two colourings of the tetrahedron are considered the same if they are identical after possibly rotating the tetrahedron.

• A. $24$
• B. $12$
• C. $8$
• D. $6$
• E. $2$

Answer 1

We have 4 different colors for 4 faces of the tetrahedron. 

We can rotate the tetrahedron. This point eliminates almost all the possible ordering because it will look same from all sides.

But there is one exception which is the mirror image of the tetrahedron.

Hence, there will be 2 possible ways. Answer (E).

Check this link for image and the real answer: https://qr.ae/pKotBt