     
\documentclass[addpoints]{exam}
    


\usepackage{amsfonts}
\usepackage{amsmath}
\sloppy


\begin{document}

  \pagestyle{headandfoot}
  \runningheadrule
  \firstpageheader{ Math 109 }{ Homework 6 }{ November 22, 2018 }
  \runningheader{ Math 109 }{ Homework 6, Page \thepage\ of \numpages}{ November 22, 2018 }

  \firstpagefooter{}{}{}
  \runningfooter{}{}{}
  \begin{flushright}
    \makebox[0.4\textwidth]{Name: \enspace\hrulefill}

    \vspace{0.2in}
    \makebox[0.4\textwidth]{Pid:\enspace\hrulefill}
  \end{flushright}

  \begin{questions}
    \question[10]
      Construct a bijection from $\mathbb{N}$ to $\mathbb{N} \times [3]$.

      \begin{solution}[\stretch{1}]
      \end{solution}
      \newpage
    \question[10]
      Show that $\sum\limits_{m = 0}^n \binom{m}{k} = \binom{n + 1}{k + 1}$.

      \begin{solution}[\stretch{1}]
      \end{solution}
      \newpage
  \end{questions}
\end{document}