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% ------------------------------------------------------------------------
% LaTeX      +++ Kay, March 2005 ************
% ------------------------------------------------------------------------
%
% ------------------------------------------------------------------------
\documentclass[12pt,a4paper]{article}

\usepackage[cp1251]{inputenc}
\usepackage{amsfonts}

\author{Kostya Yusenko}
\title{Interesting Math}
\date{02.03.05}

\newtheorem{pr}{Proposition}

\begin{document}

\maketitle

%\section*{Introduction}

\section{2+2=5}

Now I am going to prove that $2+2=5$. So

\begin{pr}
  $$2+2=5$$
\end{pr}
\emph{Proof.} Consider the right equation $4:4=5:5$. From this
equation it follows that $4(1:1)=5(1:1)$. Since (1:1)=1 we obtain
$4=5$, and it means that $2+2=4=5$. Proposition is proved.

\section{The Rate of exchange}

It is  well-known that Canada and USA are neighbors. The government of
Canada has debased the rate of American dollar down to 90 Canadian
cents. The government of USA, in one's turn, also has debased
Canadian dollar down to 90 American cents:

1 Amer  = 90 Can cents

1 Can   = 90 Amer cents

Let somebody live on boundary between USA and Canada. He has 1
Canadian dollar. And let a bottle of beer cost 10 cents in
both of countries. 10 American cents in USA and 10 Canadian cents
in Canada.

So, this man goes to Canada, drinks a bottle of beer, and gives 1
 Canadian dollar to seller. Seller offers him 90 Canadians cents or
 1 American dollar. He takes 1 dollar and goes to America where
 drinks beer and takes Canadian dollar. This process can last
 endless. The question is who pays for the beer? :)

\section{Life is just a long holiday for pupils:)}

Now I am going to calculate how many days pupils spend for studing every year.

Let's see:
\begin{enumerate}
    \item For preparing to sleep, sleeping and waking up we use
$8$ hours or $\frac{2}{3}$ of a day. It means 146 days in a
year. For other things we have $366-146=220$ days.
    \item Breakfast, dinner, lunch, supper: all it takes about 1
    hour and 15 minutes every days. Or 20 days every year.
    220-20=200.
    \item Reading newspapers and books, Watching TV - all it takes
    about 1.5 hour every day. Or 15 days every year. 200-15=185.
    \item The road to school and rest take 1.5 hour per
    days. Or 20 days every year. 185-20=165.
    \item Also we have 52 Sundays every year. 165-52=113. 71days of  summer holidays. 113-75=38.
    \item  15 days of winter, and 15 days of autumn and spring holidays. 38-30=8
    \item New Year, Christmas, Easter and other holidays - it is 8
    day per year. 8-8=0.
\end{enumerate}

It takes a proving that pupils don't studing at scholl :)

That's all :))

\section {Train of food}

It is funny but every people eat whole train of food during life. Let's calculate:

\begin{enumerate}
      \item 10.000 lt of water
      \item 1000 kg of fats
      \item 7000 kg of  bread
      \item 2000 kg of meat
      \item 4000 kg of fish
      \item 5000 kg of potatoes
      \item 5000 eggs
      \item 3000 lt of milk
      \item 500 kg of sugar
      \item 500 kg of salt

\item + Vegetables, tea, fruits, chees, koffe +....

\end{enumerate}

\section {Puzzle}

The father and his son was going to visit some city. But unfortunally they met with accident on the road.  Father died on the road.
     And son was  delivered to hospital. When the main Surgeon of that hospital had seen patient he cried:
     "It is my son".

How it can be?

\end{document}