mathematics?

How many different ways can King Arthur and his 9 sit

Gentlemen around a round table? (Considering the rotations equal

on the table that keep the same neighbors seated to the left or

right of each person).

6 Answers

Relevance
  • 2 months ago

    The number of different ways=10P10/10=9!=362880.

  • 2 months ago

    Well, I read this in the same way as Puzzling.

    King Arthur and his 9 knights gives 10 objects in total

    Given n items, they can be arranged in n! ways

    However, the n items can produce the same circular arrangement in n ways, so our total is:

    n!/n => (n - 1)!

    So, with n = 10 we have 9! = 362,880

    Note: A very rare mistake from az_lender who's answers are always first rate. As YA took away the comments option this is the only way to commend others.

    :)>

  • 2 months ago

    As I understand the question, the group consists of King Arthur and 9 knights.

    Have King Arthur sit down and he defines the orientation of the table. Everyone else sits relative to him.

    There are 9 places for the first knight.

    There are 8 places for the second knight.

    ...

    There are 2 places for the eighth knight.

    There is 1 place for the ninth knight.

    9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

    = 362,880 ways

  • 2 months ago

    az_lender was close but made an arithmetic error.

    8*7*6*5*4*3*2*1 = 56*120 = 6720

    s/b

    8*7*6*5*4*3*2*1 = 8! = 56*720 = 40320

  • How do you think about the answers? You can sign in to vote the answer.
  • 2 months ago

    So, sit King Arthur anywhere he wants.  Then his right-hand neighbor is one of 8, and the right-hand neighbor of the right-hand neighbor is one of 7, etc.  So the answer is

    8*7*6*5*4*3*2*1 = 56*120 = 6720

  • 2 months ago

    362880 ways     

Still have questions? Get your answers by asking now.