d) Prove that 3n + 2 is the minimum number of campers the counsellor needs to solve her problem. To prove this, show that with only 3n + 1 campers the counsellor cannot solve her problem. Start by using the pigeonhole principle as depicted below. Note: After you complete this proof you can use the fact that 3n + 2 is the minimum number of campers to quickly solve the campers' problem in the future for n liars, n a 1 . Hint: Reference the proof that showed with only 7 campers and n = 2 liars the counsellor cannot solve her problem. A very similar proof that worked in the case of n = 2 will also work in the general case. Pigeons g Campers ; Holes gPaths; @