Thank you for your solutions "Can fox catch rabbit" (There are five holes in a line. One of them is occupied by a rabbit. Each night, the rabbit moves to a neighboring hole, either to the left or to the right. Each morning, a fox get to inspect a hole of its choice. What strategy would ensure that the fox can eventually caught rabbit?) but I can't any idea these questions:
1)Let's have 5 holes again, but this time they should be circular instead of side by side; so the rabbit can jump from hole 1 to hole 5. Does the fox have a strategy that guarantees catching the rabbit?
2)In which configuration of n holes does the fox have a strategy that guarantees catching the rabbit?
3)Let's have 5 holes and they are lined up, but the rabbit can stay in the hole at night. Can the fox guarantee to catch the rabbit?