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# 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

- Wayne DeguManLv 72 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.

:)>

- PuzzlingLv 72 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

- nbsale (Freond)Lv 62 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

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- az_lenderLv 72 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