I'm typesetting a document with more than 100 chapters in it (don't ask, I didn't write it!). The table of contents comes out ugly, because it seems the distance between the chapter number and the chapter title is intended for two-digit chapters only. Once we hit a three digit chapter number, the last digit of the number overwrites the chapter title. How can this be modified? What variables control the width of the chapter number? Any fixes?

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You could use the titletoc package (which is a companion for titlesec).

From the titlesec/titletoc manual page 18:

\titlecontents{<section>}[<left>]{<above>}
{<before with label>}{<before without label>}
{<filler and page>}[<after>]


Example:

\documentclass[a4paper]{book}
\usepackage[english]{babel}
\usepackage{titletoc}
\usepackage{blindtext}
{\titlerule*[0.3pc]{.}\contentspage}
\begin{document}
\tableofcontents
\blinddocument
\end{document}

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The tocstyle package (included in KOMA-script) by default automatically calculates the needed indentation for chapter and other sectioning numbers in the ToC. (It needs several LaTeX runs to do so.)

\documentclass{report}

\usepackage{tocstyle}
\usetocstyle{standard}

\begin{document}

\tableofcontents

\setcounter{chapter}{5000}

\chapter{foo}

\end{document}

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If you are satisfied with the normal typesetting of the book class, you can do with "minimal" effort:

\usepackage{etoolbox}
\makeatletter
\patchcmd{\l@chapter}{1.5em}{2em}{}{}
\makeatother


You may also have a look at the memoir class, which must be considered for a 100+ chapter project; it has tools for customizing every aspect of a book, for example

\setlength{\cftchapternumwidth}{2em}


would suffice.

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