Solution
The Feuding Knights
Show the problem again
Eight knights, including Sir Agravaine and Sir Bedivere, sit at a round table with eight seats. Seatings that differ only by a rotation are considered the same (mirror images count as different). In how many ways can they be seated so that Agravaine and Bedivere do not sit next to each other? Give an integer.
Worked solution
The answer is 3600. Rotations are factored out by fixing Agravaine's seat. Of the 7 remaining seats, 2 are next to him, so Bedivere has 5 allowed seats. The other six knights fill the remaining six seats in 6! = 720 ways. Total: 5 × 720 = 3600. (Check: the unrestricted count is 7! = 5040, and the adjacent seatings number 2 × 6! = 1440.)
Source: Classic counting exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.