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Name (Last, First): $\underline{\hspace{3in}}$ \hfill Student ID: $\underline{\hspace{2in}}$

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{\small
  \href{\myurl}{Dror Bar-Natan}:
  \href{\myurl/classes/}{Classes}:
  \href{\myurl/classes/\#1516}{2015-16}:
  \href{\myurl/classes/16-475-ProblemSolving}{MAT 475 Problem Solving Seminar}:
  \hfill\url{http://drorbn.net/16-475}
}

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{\large\bf Quiz 7} on March 10, 2016: ``Divide into Cases''. You have 30 minutes to solve as much as you can of the following two problems. Please write on both sides of the page. \hfill {\bf Good Luck!}

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\noindent{\bf Problem 1 (Larson's 1.7.8)}. Determine $F(x)$, if for all real $x$ and $y$, $F(x)F(y)-F(xy)=x+y$.

\noindent{\bf Problem 2 (Larson's 2.5.11a).} Let $R_n$ denote the number of ways of placing $n$ nonattacking rooks on an $n\times n$ chessboard so that the resulting arrangement is symmetric about a $90^\circ$ clockwise rotation of the board about its centre. Show that if $k$ is a natural number, then $R_{4k}=(4k-2)R_{4k-4}$, and $R_{4k+1}=R_{4k}$, and $R_{4k+2}=R_{4k+3}=0$.

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