The Association of Tennis Professionals (ATP) ranks 200 men's tennis players and separately ranks 200 women's...
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The Association of Tennis Professionals (ATP) ranks 200 men's tennis players and separately ranks 200 women's tennis players. There are no ties in either ranking. Suppose that 20 of the 200 ATP-ranked men and 20 of the 200 ATP- ranked women register for a mixed doubles tournament (i.e., a tourna- ment in which each team will consist of one man and one woman). Prove that among these 40 players the tournament organizers can form two non- overlapping mixed doubles teams with the same average ranking. That is, prove that there are two distinct men m1 and m2 and two distinct women wi and w2 in the tournament such that rank(m1) + rank(w1) rank(m2) + rank(w2) 2 The Association of Tennis Professionals (ATP) ranks 200 men's tennis players and separately ranks 200 women's tennis players. There are no ties in either ranking. Suppose that 20 of the 200 ATP-ranked men and 20 of the 200 ATP- ranked women register for a mixed doubles tournament (i.e., a tourna- ment in which each team will consist of one man and one woman). Prove that among these 40 players the tournament organizers can form two non- overlapping mixed doubles teams with the same average ranking. That is, prove that there are two distinct men m1 and m2 and two distinct women wi and w2 in the tournament such that rank(m1) + rank(w1) rank(m2) + rank(w2) 2
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Related Book For
Accounting
ISBN: 978-0324188004
21st Edition
Authors: Carl s. warren, James m. reeve, Philip e. fess
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