A simple section exercise section

Question

What I want seems pretty simple, but I was not able to find a satisfactory answer.

What I want is something like this

\section{Foo}
A bunch of definitions, theorems, remarks, etc.
\begin{exercise}
\ex\label{ex:foo:t1} Show that this is that.
\begin{ans}
This is that by casual observation.
\end{ans}
\ex Show that is this
\begin{ans}
Just reverse the answer to exercise \ref{ex:foo:t1}.
\end{ans}
\end{exercise}

The output should be something like:

1 Foo

A bunch of definitions, theorems, remarks, etc.

Exercises

1. Show that this is that.

   Ans: This is that by casual observation.

2. Show that is this

   Ans: Just reverse the answer to exercise 1.

I also need some flexibility in numbering. For example, with a few changes to the preamble, the output could be:

1 Foo

A bunch of definitions, theorems, remarks, etc.

Exercises For Section 1

1.1 Show that this is that.

Ans: This is that by casual observation.

1.2 Show that is this

Ans: Just reverse the answer to exercise 1.1.

Answer 1

Here's an implementation using the enumitem to do some of the lifting with formating:

In the code below, we have:

\newlist{exercise}{enumerate}{5}
\setlist[exercise]{label*=\arabic*.,ref=\arabic*,before={\subsection*{Exercises}}}

This defines a list-like environment called exercise.

The next bit,

% copy \item into \ex
\let\ex\item

defines \ex as \item.

Finally, we define an ans environment:

% a simple ans environment
\newenvironment{ans}{\par Ans:}{}

Here's the complete code:

% arara: pdflatex
% !arara: indent: {overwrite: yes}
\documentclass{article}

% use the enumitem package to ease the list-like
% definition of the exercise environment
\usepackage{enumitem}
\newlist{exercise}{enumerate}{5}
\setlist[exercise]{label*=\arabic*.,ref=\arabic*,before={\subsection*{Exercises}}}

% copy \item into \ex
\let\ex\item

% a simple ans environment
\newenvironment{ans}{\par Ans:}{}

\begin{document}
\section{Foo}
A bunch of definitions, theorems, remarks, etc.
\begin{exercise}
    \ex\label{ex:foo:t1} Show that this is that.
    \begin{ans}
        This is that by casual observation.
    \end{ans}
    \ex Show that is this
    \begin{ans}
        Just reverse the answer to exercise \ref{ex:foo:t1}.
    \end{ans}
\end{exercise}
\end{document}

Regarding your requirements for numbering flexibility, if you write:

\setlist[exercise]{label*=\thesection.\arabic*.,ref=\thesection.\arabic*,before={\subsection*{Exercises}}}

then you obtain:

If you reach a point in the future when you need to separate the answers from the questions, then you might like to look at the answers package; here's a link to questions tagged with related questions: https://tex.stackexchange.com/questions/tagged/answers.