Question 6
i. $15$ chairs are equally placed around a circular table on which are name cards for $15$ guests. The guests fail to notice these cards until after they have sat down, and it turns out that no one is sitting in the correct seat. Prove that the table can be rotated so that at least two of the guests are simultaneously correctly seated.
ii. Give an example of an arrangement in which just one of the $15$ guests is correctly seated and for which no rotation correctly places more than one person.
ii. Give an example of an arrangement in which just one of the $15$ guests is correctly seated and for which no rotation correctly places more than one person.