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pow:problem2s21

Problem 2 (due Monday, March 15)

Let $\Gamma$ be the set of all points $(a,b)$ on the cartesian plane such that $a,b$ are positive integers not exceeding $100$. A subset $H$ of $\Gamma$ is called rounded if for any two points $(a,b)$ and $(A,B)$ in $H$, either $a>A-10$ and $b>B-10$ or $A>a-10$ and $B>b-10$. What is the largest size of a rounded subset of $\Gamma$?

Ashton Keith is the only person who submitted a solution. The main idea of his solution is correct and it is essentially the same as the one in our solution (though, due to some errors in calculations, the provided answer is not correct). Detailed solution is discussed in the following link Solution.