121 lines
3.0 KiB
TeX
Executable File
121 lines
3.0 KiB
TeX
Executable File
\documentclass[
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solutions,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage{../../resources/macros}
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\makeatletter
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\newcommand{\thisone}{
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\if@solutions
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{\color{red} $\Leftarrow$ \texttt{this one}}
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\else\fi
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}
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\title{Warm-Up: The Gallery}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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A museum curator is arranging seven photographs on a gallery wall in accordance with the photographer's requirements.
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They are titled as follows: Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia.
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The photograph's requirements are as follows:
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\begin{itemize}
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\item Gardenias must be immediately before Katydid.
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\item Hibiscus must be somewhere before Katydid but cannot be the first photograph.
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\item Irises and Lotus must be next to one another.
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\item Magnolia must be one of the first three photographs.
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\item Fence must be either first or seventh.
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\end{itemize}
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\problem{}
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Which of the below could be a valid ordering? \par
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\note[Note]{We denote each painting by the first letter of its title.}
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\begin{itemize}
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\item \texttt{FHGMKIL}
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\item \texttt{HMGKILF}
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\item \texttt{ILMHGKF} \thisone{}
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\item \texttt{LMIHGKF}
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\item \texttt{MFHGKLI}
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\end{itemize}
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\vfill
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\problem{}
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If Irises is immediately before Gardenias, which of the following could be true?
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\begin{itemize}
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\item Gardenias is fourth
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\item Hibiscus is fourth
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\item Irises is third
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\item Lotus is second
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\item Magnolia is third \thisone{}
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\end{itemize}
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\vfill
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\problem{}
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The ordering of the photographs is fully determined if...
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\begin{itemize}
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\item Gardenias is fourth
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\item Hibiscus is second
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\item Irises is second
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\item Lotus is first \thisone{}
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\item Magnolia is third
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\end{itemize}
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\vfill
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\pagebreak
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\problem{}
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If Magnolia is second, what CANNOT be true?
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\begin{itemize}
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\item Hibiscus is third
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\item Hibiscus is fourth \thisone{}
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\item Hibiscus is fifth
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\item Gardenias is fourth
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\item Gardenias is sixth
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\end{itemize}
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\vfill
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\problem{}
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Katydid cannot be in which position?
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\begin{itemize}
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\item Third \thisone{}
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\item Fourth
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\item Fifth
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\item Sixth
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\item Seventh
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\end{itemize}
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\vfill
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\problem{}
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If Gardenias is fourth, what must be true?
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\begin{itemize}
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\item Fence is first \thisone{}
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\item Hibiscus is third
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\item Irises is seventh
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\item Magnolia is first
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\item Magnolia is second
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\end{itemize}
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\vfill
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\problem{}
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Which one of the following,
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if substituted for the second condition,
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would have the same effect in determining the
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arrangement of the photographs?
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\begin{itemize}
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\item If Fence is seventh, Hibiscus is second
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\item Gardenias is somewhere after Hibiscus, and either Fence or Magnolia is first
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\item Hibiscus must be somewhere between the first and sixth photographs
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\item Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias \thisone{}
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\item Katydid is somewhere after Hibiscus, which must be after Fence.
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\end{itemize}
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\vfill
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\pagebreak
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\end{document} |