A bridge club has $10$ members. Every day, four members of the club get together and play one game of bridge. Prove that after two years, there is some particular set of four members that has played at least four games of bridge together.
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1Any thoughts? How many groups of $4$ are there? If each group plays $3$ or fewer times together, how many days might they all play? – lulu Feb 10 '19 at 19:50
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$210$ ways to pick $4$ people from $10$, three times this is $630$. There are more than this many days in $2$ years therefore a for at least one of the $210$ groups has played at least $4$ times by the end of $2$ years.
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