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\begin{document}
\headers{Math378}{Quiz 4}{Wed. Feb 18, 2026}
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\noindent
\hfill Name: \underline{\hspace{3.5in}} 

\noindent
\textbf{Directions:} Show all work.  

\begin{enumerate}
	\item\points{4} Let $S$ be a set of $5$ points in an equilateral triangle with side length $2$.  Prove that $S$ contains a pair of points that are at distance at most $1$.
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	\end{center}
	\vfill
	
	\newpage
	\item\ppoints{2}{3} Recall that two integers $x$ and $y$ are \emph{relatively prime} if their greatest common divisor is $1$.
	\begin{enumerate}
		\item Find a maximum size subset of $\{1,\ldots,8\}$ such that no two elements in $A$ are relatively prime.  Prove your answer is correct.
		\vspace{5cm}
		
		\item Find a maximum size subset of $\{1,\ldots,2n\}$ such that no two elements in $A$ are relatively prime.  Prove your answer is correct.
		\vfill
	\end{enumerate}
\end{enumerate}
\end{document}
