examday

/TMUA

Eight chairs are arranged in a circle, and some of them are occupied.

A chair is called crowded if both of the chairs next to it are occupied. (A chair may be crowded whether or not it is itself occupied.)

Which of the following statements is/are true?

• I It is possible for exactly $4$ chairs to be occupied with no chair crowded.
• II If $5$ chairs are occupied then at least one chair must be crowded.
• III If exactly $2$ chairs are occupied then no chair is crowded.