% Written By Enoch Yu
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\fancyhead[L]{AMC 8 Class}
\fancyhead[C]{Problem Set 4}
\fancyhead[R]{Enoch Yu}
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\title{Problem Set 4}
\author{Enoch Yu}
\date{1 September 2025}

\begin{document}

Name:

Date:

\section*{\textcolor{ForestGreen}{Easy}}
\begin{minipage}[t][0.4\textheight][t]{\textwidth}
\subsection*{Problem 1.} % Made by Enoch (13*17*19)
{\color {Gray}
Prime factorize $4199$.
}

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\textbf{Solution.}

\end{minipage}


\begin{minipage}[t][0.4\textheight][t]{\textwidth}
\subsection*{Problem 2.} % Made by Enoch (1000*1001/2)
{\color {Gray}
Find the sum of all natural numbers from 1 to 1000.
}

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\textbf{Solution.}

\end{minipage}


\newpage
\section*{\textcolor{YellowOrange}{Moderate}}
\begin{minipage}[t][0.45\textheight][t]{\textwidth}
\subsection*{Problem 3.} % Made by Enoch (-500)
{\color {Gray}
Compute the sum:
\[
5 - 10 + 15 - 20 + \cdots - 1000.
\]
}

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\textbf{Solution.}

\end{minipage}

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\subsection*{Problem 4.} % Made By Enoch (8)
{\color {Gray}
How many factors does $4199$ have?
}

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\textbf{Solution.}

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\section*{\textcolor{BrickRed}{Challenging}}
\begin{minipage}[t][0.45\textheight][t]{\textwidth}
\subsection*{Problem 5.} % Made By Enoch
{\color {Gray}
Prove that $100^{10} = 2^{20} \cdot 5^{20}$.
}

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\textbf{Solution.}

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\begin{minipage}[t][0.45\textheight][t]{\textwidth}
\subsection*{Problem 6.} % Made By Enoch
{\color {Gray}
Explain and prove Pythagorean Theorem in your own word.
}

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\textbf{Solution.}

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\end{document}

