Question

If he 4 sides of a square are to be colored by colors. How many different colourings with 50 colours are there if two arrangements that can be obtained from each other by rotation are identical?

(a) 773762

(b) 363563

(c) 4536822

(d) 1563150

This question was addressed to me in an interview.

My doubt is from Groups in division Groups of Discrete Mathematics

Answer 1

Correct choice is (d) 1563150

Explanation: There are m^4 + m^2 + 2m elements after performing all rotations. Dividing this by the number of transformations 4 produces the desired number of distinct colorings \(\frac{m^4 + m^2 + 2m}{4}\). Hence, the number of distinct colorings with 50 colors is 1563150.