Seating five knights at a round table

Question

Five knights sit around a round table with no head seat. Seatings that differ only by a rotation are considered the same. How many distinct seatings are there?

Accepted Answer

Anchor the circle by seating one knight first; this removes the rotational symmetry. The remaining 4 knights then fill the 4 seats around the table in 4! = 24 ways. Equivalently, \dfrac{5!}{5} = \dfrac{120}{5} = 24 = (5-1)!. Takeaway. For a round table with rotations equivalent, fix one person and arrange the rest: (n-1)!. Five knights give 4! = 24.

Seating five knights at a round table

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