Pigeonhole principle with cartesian product – math.stackexchange.com

Given sets $A=\{1,2,\dots ,10\}, B=\{1,2,\dots,12\}$. Let $S\subset A\times B$ s.t. $|S|=61$. Prove that there exist three pairs $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ in $S$ which fulfill:$$ ...

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