Question

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

(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

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