20 Mar 2013

Friends Round a Table: Middle Secondary Mathematics Competition Question

Ten friends are going out to dinner to celebrate their graduation. Alice has two close friends, Brenda and Clarice, and the three of them wish to sit next to each other. However, David also wants to sit next to Alice. If all ten friends sit around one large circular table, how many possible unique seating arrangements are there that make all four people happy?

Note that the questions says nothing about the chairs being numbered, or anything else that breaks the symmetry of the round table, so you may count all rotational symmetries as one arrangement.

Level: Middle Secondary (Yellow)

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