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Keneth Rosen
ankit aingh
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May 12, 2018
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Show that among any n + 1 positive integers not exceeding 2n there must be an integer that divides one of the other integers.
pigeonhole-principle
combinatory
ankit aingh
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May 12, 2018
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https://math.stackexchange.com/questions/2077929/induction-to-prove-that-a-set-of-n1-integers-between-1-and-2n-has-at-leas
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Ayush Upadhyaya
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Keneth Rosen ex 10 pg 350
During a month with 30 days, a baseball team plays at least one game a day, but no more than 45 games. Show that there must be a period of some number of consecutive days during which the team must play exactly 14 games. proof is given in rosen but I am unable to get it. It would be good if someone could give a proof of it in a better way.
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An arm wrestler is the champion for a period of 75 hours. (Here, by an hour, we mean a period starting from an exact hour, such as 1 P.M., until the next hour.) The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.
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A drawer contains a dozen of brown and dozen of black socks,all unmatched.A man takes socks out at random in the dark. How many socks must he take out to be sure that he has atleast two black socks ?
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