Added warmups

This commit is contained in:
Mark 2024-01-08 11:26:44 -08:00
parent cec0cb5dc5
commit df71c8676f
Signed by: Mark
GPG Key ID: C6D63995FE72FD80
2 changed files with 110 additions and 0 deletions

21
Misc/Warm-Ups/fmod.tex Executable file
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\documentclass[
solutions,
hidewarning,
singlenumbering,
nopagenumber
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}
\title{Warm-Up: \texttt{fmod}}
\subtitle{Prepared by \githref{Mark} on \today.}
\begin{document}
\maketitle
\problem{}
I'm sure you're all familiar with how \texttt{mod(a, b)} and \texttt{remainder(a, b)} work with integers. \par
Devise an equivalent for floats (i.e, real numbers).
\end{document}

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Misc/Warm-Ups/painting.tex Executable file
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\documentclass[
solutions,
hidewarning,
singlenumbering,
nopagenumber
]{../../resources/ormc_handout}
\usepackage{../../resources/macros}
\usepackage[linguistics]{forest}
\title{Warm-Up: Painting}
\subtitle{Prepared by \githref{Mark} on \today.}
\begin{document}
\maketitle
\problem{}
You have a painting on a string. \par
Hang the painting on two nails so that if either is removed, the painting falls. \par
\vspace{2mm}
You may detach the string as you hang the painting, but it must be re-attached once you're done.
\note{The solution to this problem isn't an out-of-the-box trick, it's a clever wrapping of the string.}
\begin{center}
\begin{tikzpicture}[scale=2.0]
\draw[line width = 0.5mm]
(0, 1) --
(2, 1) --
(2, 0) --
(0, 0) --
cycle
;
\draw[line width = 0.5mm, dotted]
(0.1, 1) --
(1, 1.5) --
(1.9, 1)
;
\fill (1, 1.5) circle[radius = 0.25mm];
\draw[line width = 0.2mm]
(0.66, 0.66) --
(0.66, 0.35) --
(0.60, 0.1)
(0.72, 0.1)--(0.66, 0.35)
;
\draw[line width = 0.2mm]
(0.66, 0.575) --
(0.6, 0.475) --
(0.525, 0.575)
(0.66, 0.575) --
(0.72, 0.475) --
(0.795, 0.575)
;
\fill[color=white] (0.66, 0.66) circle[radius = 0.8mm];
\draw (0.66, 0.66) circle[radius = 0.8mm];
\end{tikzpicture}
\end{center}
\begin{solution}
Say we have a left nail and a right nail. The path of the string is as follows:
\begin{itemize}
\item Start on the left
\item Move over both nails, wrap right nail cw
\item Wrap left nail ccw
\item Wrap right nail ccw
\item Exit downwards, in between both nails
\end{itemize}
\end{solution}
\end{document}