Logic Puzzle
Författare:
Tejas Joshi
Last Updated:
för 8 år sedan
Licens:
Creative Commons CC BY 4.0
Sammanfattning:
Cute logic puzzle.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
Cute logic puzzle.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[12pt]{article}
\usepackage{color,fancyhdr,ifthen,amssymb,amsfonts,amsmath}
\pagestyle{fancy}
\setlength{\topmargin}{-.5in}
\setlength{\textheight}{9in}
\setlength{\oddsidemargin}{0in}
\setlength{\evensidemargin}{0in}
\setlength{\textwidth}{6.5in}
\setlength{\headwidth}{\textwidth}
\parindent=0in
\newcounter{questionNumber}
\setcounter{questionNumber}{1}
\newcommand{\headandfoot}[3]{\lhead{#1}\chead{#2}\rhead{\ifthenelse{\isodd{\thepage}}{Dr. Matsko {\hspace{.25in}}}{}}
\lfoot{IMSA}\cfoot{\thepage}\rfoot{#3}}
\linespread{1.75}
\newcommand{\question}[6]{\noindent\thequestionNumber.\quad #1\\[.1in]
(a) #2 \\
(b) #3 \\
(c) #4 \\
(d) #5 \\
(e) #6
\vspace{.25in}\addtocounter{questionNumber}{1}}
\headandfoot{Advanced Problem Solving}{ Original Problem}{9.4.12}
\begin{document}
\begin{center}\textbf{Logic without Lies}
\\-----Tejas Joshi----- \\
\end{center}
A wolf, sheep, and a sentient cabbage were caught crossing a small river. During a later interrogation, each gave statements about the incident.
The police know the following facts:
\begin{enumerate}
\item One creature always tells the truth, another always lies and the third doesn't speak because it's a cabbage.
\item Before going to the river, each creature knew that they chose a hat at random from an assortment of two red caps and two blue caps total.
\item No creature ever saw its own cap, and no creature knows what color its own hat is.
\item The cabbage can't see anything (it has no eyes, just a head).
\item One creature is the gang's ringleader, and another is the police's anonymous informant. After being caught, everyone knows who the ringleader and informant were.
\item Each creature was at one side of the river when they were caught.
\end{enumerate}
Each suspect later gave the following statements:
\newline
Sheep
\begin{enumerate}
\item The ringleader couldn't possibly have seen my hat unless the wolf is the informant.
\item The cabbage was on the same side of the river as the informant, and the informant had a blue hat.
\item I can deduce that one side of the river had no blue hats and no side of the river was empty.
\end{enumerate}
Wolf
\begin{enumerate}
\item Either the informant or the ringleader but not both was on the same side of the river as the cabbage.
\item The sheep is the informant, and the informant has a blue hat
\item I can deduce that either no-one knows their own hat color or the ringleader and informant both do.
\end{enumerate}
What color is the cabbage's hat?
\end{document}