Added Moscow Puzzles

Misc/Moscow Puzzles/main.tex

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+% https://git.betalupi.com/Mark/latex-packages
+% use [nosolutions] flag to hide solutions.
+% use [solutions] flag to show solutions.
+% Last built with version 1.1.0
+\documentclass[
+	solutions
+]{ormc_handout}
+
+\usepackage{subfiles}
+\usepackage{graphicx}
+\graphicspath{ {./images} }
+
+\begin{document}
+
+	\maketitle
+		<Intermediate 2>
+		<ORMC Summer Sessions>
+		{Warm - Up}
+		{
+			Prepared by Mark on \today \\
+			\medskip
+			These problems were originally found in \\
+			Boris Kordemsky's \textit{The Moscow Puzzles}
+		}
+
+	\subfile{problems/217}
+	\vfill
+	\pagebreak
+
+	\subfile{problems/101}
+	\vfill
+	\pagebreak
+
+\end{document}

Misc/Moscow Puzzles/problems/101.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{The Courageous Garrison}
+
+	A courageous garrison was defending a snow fort. The commander arranged his forces as shown in the square frame (the inner square showing the garrison's total strength of 40 boys): 11 boys defending each side of the fort.
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=12cm]{101a}
+	\end{figure}
+
+	The garrison ``lost'' 4 boys during each of the first, second, third, and fourth assaults and 2 during the fifth and last. But after each charge 11 boys defended each side of the snow fort. How?
+
+	\vfill
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=4cm]{101b}
+	\end{figure}
+
+\end{document}

Misc/Moscow Puzzles/problems/110.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{Knight's Move}
+
+	To solve this problem you need not be a chess player. You need only know the way a knight moves on the chessboard: two squares in one direction and one square at right angles to the first direction. The diagram shows 16 black pawns on a board.
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=12cm]{110}
+	\end{figure}
+
+	Can a knight capture all 16 pawns in 16 moves?
+
+\end{document}

Misc/Moscow Puzzles/problems/120.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{One Hundred and Fourty-Five Doors}
+	A prisoner was thrown into a medieval dungeon with 145 doors. Nine, shown by black bars, are locked, but each one will open if before you reach it you pass through exactly 8 open doors. \\
+	You don't have to go through every open door but you do have to go through every cell and all 9 locked doors. If you enter a cell or go through a door a second time, the doors clang shut, trapping you. \\
+
+	\medskip
+
+	The prisoner (in the lower right corner cell) had a drawing of the dungeon. He thought a long time before he set out. He went through all the locked doors and escaped through the last, upper left corner one. What was his route?
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=8cm]{120}
+	\end{figure}
+
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=8cm]{120}
+	\end{figure}
+
+\end{document}

Misc/Moscow Puzzles/problems/121.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{How Does the Prisoner Escape?}
+
+	This dungeon has $49$ cells. In $7$ cells ($A$ to $G$ in the diagram) there is a locked door (black bar). The keys are in cells $a$ to $g$ respectively. The other doors open only from one side, as shown. \\
+
+	\medskip
+
+	How does the prisoner in cell $O$ escape? He can pass through any door any number of times and need not unlock the doors in any special order. His aim is to get the key from cell $g$ and use it to escape through cell $G$
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=8cm]{121}
+	\end{figure}
+	\vfill
+
+	Here's an extra copy of the dungeon:
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=8cm]{121}
+	\end{figure}
+
+\end{document}

Misc/Moscow Puzzles/problems/217.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{Mutual Aid}
+
+	During the rebuilding after World War II, the Soviet Union was short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors. How many tractors did each station originally have?
+
+\end{document}

Misc/Moscow Puzzles/problems/239.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{One Hundred and Fourty-Five Doors}
+
+	Volodya asked, ``What plane did you fly during the air parade?'' His father sketched a formation of 9 planes.
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=9cm]{239}
+	\end{figure}
+
+	``The number of planes to the right of me multiplied by the number of planes to the left of me is 3 less than it would have been if my plane had been 3 places to the right of me.'' How did Volodya solve the problem?
+
+\end{document}

Misc/Moscow Puzzles/problems/252.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{An Elephant and a Mosquito}
+
+	Does the weight of an elephant equal the weight of a mosquito? Let $x$ be the weight of an elephant, and $y$ that of a mosquito.
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=10cm]{252}
+	\end{figure}
+
+	Call the sum of the two weights $2v$, then $x + y = 2v$.
+
+	From this equation we can obtain two more:
+
+	\[
+		x - 2v = -y \text{; } x = - y + 2v
+	\]
+
+	Multiply:
+	\[
+		x^2 - 2vx = y^2 - 2vy
+	\]
+
+	Add $v^2$:
+	\[
+		x^2 - 2vx + v^2 = y^2 - 2vy + v^2 \text{, or } (x - v)^2 = (y - v)^2
+	\]
+
+	Take square roots:
+	\[
+		x - v = y - v \text{; } x = y
+	\]
+
+	That is, the elephant's weight ($x$) equals the mosquito's weight ($y$). What is wrong here?
+
+
+\end{document}

Misc/Moscow Puzzles/problems/255.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{The Lucas Problem}
+
+	This problem was invented by Edouard Lucas, a French nineteenth-century mathematician. \\
+	``Every day at noon,'' Lucas said, ``a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many New York-Le Havre ships will the ship leaving Le Havre today meet during its journey to New York? Can you answer graphically?
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=10cm]{255}
+	\end{figure}
+
+
+\end{document}

Misc/Moscow Puzzles/problems/263.tex

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+\documentclass[../main.tex]{subfiles}
+
+\begin{document}
+
+	\problem{A Shooting Match}
+	Andryusha, Borya, and Volodya each fired 6 shots, and each got 71 points.
+
+	\begin{figure}[h]
+		\centering
+		\includegraphics[width=8cm]{263}
+	\end{figure}
+
+	Andryusha's first 2 shots got 22 points and Volodya's first shot got only 3 points. \\
+	Who hit the bull's-eye?
+
+\end{document}