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    Daily ChallengeHardCombinatorics

    How many ways can 8 people be seated at a round table?

    De quantas maneiras 8 pessoas podem sentar-se à volta de uma mesa redonda?

    Answer options

    Practice page — XP is earned on the Daily Challenge on the home page.

    Solution

    Circular permutations: (8-1)! = 7! = 5040

    Two round tables drawn side by side, each with eight seats spaced equally around it and a letter in each seat. On the left table the letters run A to H clockwise from the top. The right table carries the same order, with everyone moved on by one seat, so the letter at the top is now H. An arrow between the two tables marks the turn of one place. The two pictures show the same circular arrangement.ABCDEFGHHABCDEFGturnthe same seatingthe same seating