Moved Proof techniques

Misc/Warm-Ups/snake.tex

@@ -0,0 +1,232 @@
+\documentclass[
+	solutions,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+\usepackage{ifthen}
+
+\usetikzlibrary{arrows.meta}
+\usetikzlibrary{shapes.geometric}
+\usetikzlibrary{patterns}
+
+% We put nodes in a separate layer, so we can
+% slightly overlap with paths for a perfect fit
+\pgfdeclarelayer{nodes}
+\pgfdeclarelayer{path}
+\pgfsetlayers{main,nodes}
+
+% Layer settings
+\tikzset{
+	% Layer hack, lets us write
+	% later = * in scopes.
+	layer/.style = {
+		execute at begin scope={\pgfonlayer{#1}},
+		execute at end scope={\endpgfonlayer}
+	},
+	%
+	% Arrowhead tweak
+	>={Latex[ width=2mm, length=2mm ]},
+	%
+	% Labels inside edges
+	label/.style = {
+		rectangle,
+		% For automatic red background in solutions
+		fill = \ORMCbgcolor,
+		draw = none,
+		rounded corners = 0mm
+	},
+	%
+	% Nodes
+	main/.style = {
+		draw,
+		circle,
+		fill = white,
+		line width = 0.4mm,
+		text width = 5mm,
+		align = center
+	},
+	accept/.style = {
+		draw,
+		circle,
+		fill = white,
+		double,
+		double distance = 0.5mm,
+		line width = 0.4mm,
+		text width = 5mm,
+		align = center
+	},
+}
+
+
+
+\title{Warm-Up: Snakes}
+\subtitle{Prepared by \githref{Mark} on \today}
+
+\begin{document}
+
+	\maketitle
+	\newcounter{mycounter}
+	\setcounter{mycounter}{0}
+	\newif\iftmp
+
+	\begin{center}
+	\begin{tikzpicture}[scale = 0.6]
+		\begin{scope}[layer = nodes]
+			\foreach \r in {1,3,5,7,9} {
+				\foreach \i in {1,...,10} {
+					\pgfmathparse{Mod(\i-1,10)}
+					\let\x\pgfmathresult
+					\pgfmathparse{div(\i-1,10) + \r}
+					\let\y\pgfmathresult
+					\pgfmathparse{(\r-1)*10+\i}
+					\let\z\pgfmathresult
+
+					\tmpfalse
+					\pgfmathapproxequalto{\z}{4}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{5}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{19}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{21}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{28}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{31}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{35}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{44}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{47}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{52}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{53}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{59}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{70}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{76}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{81}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{88}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{98}
+					\ifpgfmathcomparison\tmptrue
+					\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+
+					\stepcounter{mycounter}
+					\iftmp
+						\node[accept] (\arabic{mycounter}) at (2*\x, 2*\y) {
+							$\pgfmathprintnumber{\z}$
+						};
+					\else
+						\node[main] (\arabic{mycounter}) at (2*\x, 2*\y) {
+							$\pgfmathprintnumber{\z}$
+						};
+					\fi
+				}
+
+				\foreach \i in {1,...,10} {
+					\pgfmathparse{9 - Mod(\i-1,10)}
+					\let\x\pgfmathresult
+					\pgfmathparse{div(\i-1,10) + \r + 1}
+					\let\y\pgfmathresult
+					\pgfmathparse{\r*10+\i}
+					\let\z\pgfmathresult
+
+					\tmpfalse
+					\pgfmathapproxequalto{\z}{4}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{5}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{19}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{21}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{28}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{31}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{35}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{44}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{47}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{52}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{53}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{59}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{70}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{76}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{81}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{88}
+					\ifpgfmathcomparison\tmptrue
+					\else\pgfmathapproxequalto{\z}{98}
+					\ifpgfmathcomparison\tmptrue
+					\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi
+
+					\stepcounter{mycounter}
+
+					\iftmp
+						\node[accept] (\arabic{mycounter}) at (2*\x, 2*\y) {
+							$\pgfmathprintnumber{\z}$
+						};
+					\else
+						\node[main] (\arabic{mycounter}) at (2*\x, 2*\y) {
+							$\pgfmathprintnumber{\z}$
+						};
+					\fi
+				}
+			}
+		\end{scope}
+
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(4) -- +(1,0) -- +(1, 13) -- +(3, 13) -> (75);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(5) -- +(0,-1) -- +(1,-1) -- +(1,1) -- (15);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(19) -- +(1, 0) -- +(1, 5) -- + (-1, 5) -- (41);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(21) -- +(1, 0) -- +(1,-5) -- +(3, -5) -- (3);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(28) -- +(1,0) -- +(1,3) -- +(3,3) -- (50);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(31) -- +(1,0) -- +(1,-7) -- +(-3, -7) -- (8);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(35) -- +(-1,0) -- +(-1,11) -- (96);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(44) -- +(-1,0) -- +(-1,7) -- +(-3,7) -- (82);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(47) -- +(1,0) -- +(1,-3) -- +(5,-3) -- (30);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(52) -- +(-1, 0) -- +(-1, -1) -- +(-5,-1) -- +(-5,-5) -- +(-11,-5) -- (23);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(53) -- +(-1,0) -- +(-1,7) -- (94);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(59) -- +(-1, 0) -- +(-1,1) -- +(-3,1) -- +(-3,9) -- +(7, 9) -- (95);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(70) -- +(-1, 0) -- +(-1, 5) -- (91);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(76) -- +(-1, 0) -- +(-1,-1) -- +(-5,-1) -- +(-5,-5) -- +(-7,-5) -- (41);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(81) -- +(0, -1) -- +(3, -1) -- +(3, -3) -- (62);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(88) -- +(1, 0) -- +(1, -3) -- +(-1,-3) -- (67);
+		\draw[->, line width = 0.6mm, rounded corners = 2mm]
+			(98) -- +(0, 1.5) -- +(15.5, 1.5) -- +(15.5,-15) -- +(13, -15) -- (12);
+	\end{tikzpicture}
+	\end{center}
+
+\end{document}