1. Not in Book 1: You're a Math Wizard Ha Harry's competitive math team has been ranked the number one team for the past 40 days. His team competes in a math competition at least once per day and competes in no more than 60 competitions in these 40 days. Show that there is some day i and some day j such that between i and j, exactly 19 matches have been played. Hint: Let a; be the number of competitions completed by the ith day. Consider the rela- tionship between a; and aj. 1. Not in Book 1: You're a Math Wizard Ha Harry's competitive math team has been ranked the number one team for the past 40 days. His team competes in a math competition at least once per day and competes in no more than 60 competitions in these 40 days. Show that there is some day i and some day j such that between i and j, exactly 19 matches have been played. Hint: Let a; be the number of competitions completed by the ith day. Consider the rela- tionship between a; and aj