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Question: 4 you were one of four people attending a meeting...

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(4) You were one of four people attending a meeting. At the beginning of the meeting, a round of hand-shakes took place. We do not know how many hands each person shook. However, regardless of the number of hands each person shook, you think that there must be two people who shook the same number of hands.

a. First, assume that everyone shook at least one hand. Write up a pigeonhole principle-type argument to show that there must be two people who shook the same number of hands.

b. Now, suppose we don’t know whether everyone shook at least one hand. Write up a pigeonhole principle to show that there must be two people who shook the same number of hands.

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