Tabularx and \hsize column tuning

Question

In this answer : Tabularx table with multirows and multicolumns, I have discovered the \hsize possibility to tune X column width of tabularx table.

The documentation says :

Make sure that the sum of the widths of all the X columns is unchanged.

But the answer says :

\begin{tabularx}{\textwidth}{|>{\hsize=0.5\hsize}X|
                    *{3}{ >{\hsize=1.5\hsize}X|}
                        }

that makes a sum of 5 for 4 columns, and it leeds to problems if one not fill columns enought.

Questions :

• Why it works in the example and not in the following example ?

• What is the correct method to calculate the \hsizes ?

\documentclass{article}
\usepackage{tabularx}
\begin{document}
\begin{table}

\begin{tabularx}{\linewidth}{|>{\hsize=0.5\hsize}X|
                        *{3}{ >{\hsize=1.5\hsize}X|}
                            }\hline
1&2&3&4\\\hline
\end{tabularx}

\bigskip

% My proposition if correctly understood the manuel
\begin{tabularx}{\linewidth}{|>{\hsize=0.5\hsize}X|
                        *{3}{ >{\hsize=1.16667\hsize}X|}
                            }\hline
1&2&3&4\\\hline
\end{tabularx}
\end{table}
\end{document}

Answer 1

It seems you want three equal-width columns (let's denote their width by x), plus another column that's one-third as wide as the other three; denote its width by y. The combined width of the four columns should equal \linewidth.

The computation is that of barycentric coordinates: you have to solve the linear system:

3x + y = 4 % 4: number of columns of type "X"
x = 3y

It is easy to find this yields y=0.4 and x=1.2, whence the code:

\documentclass{article}
\usepackage{tabularx}
%% define a custom col. type to simplify expressing relative col. widths
\newcolumntype{H}[1]{>{\hsize=#1\hsize\arraybackslash}X}

\begin{document}

\begin{table}
\begin{tabularx}{\linewidth}{| H{0.4} | *{3}{H{1.2}|} } % 0.4+3*1.2=4
\hline
1&2&3&4\\
\hline
\end{tabularx}
\end{table}

\end{document} 

Answer 2

Bernard's answer shows how to set the values while following the rules in the tabularx documentation, but to answer your question about what happens in the table that doesn't follow the rules.

First note that as posted there is a small error as seen in the spanning column entries which are not centred in their width.

The intention of the calculation was that the width was double the natural width plus adjustment for the space and rules around the columns, but the columns that are spanned already have 1.5 multiplier applied so the spanning column needs to be 3\hsize not 2\hsize plus adjustment for the column padding. see the second table in the example her:

\documentclass{article}
\usepackage{tabularx}

\tracingtabularx
\begin{document}
\begin{table}

\begin{tabularx}{\linewidth}{@{\extracolsep{0pt}}|>{\hsize=0.5\hsize}X|
                         *{3}{>{\hsize=1.5\hsize}X|}
                            }\hline
1\dotfill X&
\multicolumn{2}{>{\hsize=\dimexpr2\hsize+2\tabcolsep+\arrayrulewidth\relax}X|}{text\dotfill X}&
4\dotfill X\\\hline
1\dotfill X&2\dotfill X&3\dotfill X&4\dotfill X\\\hline
\end{tabularx}

\bigskip

\begin{tabularx}{\linewidth}{@{\extracolsep{0pt}}|>{\hsize=0.5\hsize}X|
                         *{3}{>{\hsize=1.5\hsize}X|}
                            }\hline
1\dotfill X&
\multicolumn{2}{>{\hsize=\dimexpr3\hsize+2\tabcolsep+\arrayrulewidth\relax}X|}{text\dotfill X}&
4\dotfill X\\\hline
1\dotfill X&2\dotfill X&3\dotfill X&4\dotfill X\\\hline
\end{tabularx}


\end{table}
\end{document}

So why does the second table work as it doesn't follow either of tabularx stated rules

• Make sure that the sum of the widths of all the {\ttfamily X} columns is unchanged. (In the above example, the new widths still add up to twice the default width, the same as two standard {\ttfamily X} columns.)

• Do not use "\multicolumn" entries which cross any {\ttfamily X} column.

The reason is hinted in the tabularx documentation which follows those rules by the helpful further documentation

As with most rules, these may be broken if you know what you are doing.

Here essentially what is happening is that the initial guessed widths are too narrow as tabularx is expecting 5 columns, but the standard tabularx iterative trials to find the right widths reduces the effective number of X columns at each trial (to take account of X columns that are "hidden" by \multicolumn{c} headers and so do not affect the total table width. So it turns out that apart from causing one extra iteration of the tabularx trials the end result is a table of the right width. Note however without the multicolumn the initial bad starting point sends tabularx into a path where it never converges on a solution that gives the correct table:

\documentclass{article}
\usepackage{tabularx}

\tracingtabularx
\begin{document}
\begin{table}

\begin{tabularx}{\linewidth}{@{\extracolsep{0pt}}|>{\hsize=0.5\hsize}X|
                         *{3}{>{\hsize=1.5\hsize}X|}
                            }\hline
1\dotfill X&
?&?&
4\dotfill X\\\hline
1\dotfill X&2\dotfill X&3\dotfill X&4\dotfill X\\\hline
\end{tabularx}



\end{table}
\end{document}

so perhaps

As with most rules, these may be broken if you know what you are doing.

could have perhaps have been phrased as

As with most rules, these may be broken if you are lucky.