Question 6
The friendly beavers of Jeju leave messages for visiting neighbours using a special three-bar gate.

Four example messages are: I am home; I will return late; I will return soon; nobody is home.

Cheolsoo thinks more messages are possible by changing the bars. What is the largest number of messages?
Editorial reading of the examples: each of the three distinct bar positions can independently be across the gate or lowered at its free end.

Four example messages are: I am home; I will return late; I will return soon; nobody is home.

Cheolsoo thinks more messages are possible by changing the bars. What is the largest number of messages?
Editorial reading of the examples: each of the three distinct bar positions can independently be across the gate or lowered at its free end.