Question

(a) Imagine eight caves in a circle and two hunters. Prove the wabbit can be caught.

(b) Imagine nine caves in a grid (as shown below). The wabbit can move vertically or horizontally. For instance, if the wabbit is in cave 2 today, then tomorrow, the wabbit must be in one of caves 1, 3, or 5. Remember that the wabbit cannot stay in the same cave on consecutive days.

1	2	3
4	5	6
7	8	9

Table 1: Kill the Wabbit with 9 caves. Prove that the wabbit can be caught with three hunters.

(c) Using the same setup as part (b) but only two hunters, can the wabbit be caught? If so, give a proof. If not, explain why not.

Answer 1

Solution: