MathDB

Suppose that

10

mathematics teachers gather at a circular table with

25

seats to discuss the upcoming mathematics competition. Each teacher is assigned a unique integer ID number between

1

and

10

, and the teachers arrange themselves in such a way that teachers with consecutive ID numbers are not separated by any other teacher (IDs

1

and

10

are considered consecutive). In addition, each pair of teachers is separated by at least one empty seat. Given that seating arrangements obtained by rotation are considered identical, how many ways are there for the teachers to sit at the table?

Problem Statement