Left-aligned headers but centered entries in the remainder of the column

Question

There are three edits that I want for the table the following code gives.

First, I want the column headers left-aligned and the remaining entries in the columns centered.

Second, I would like to put {\centering\arraybackslash} in the last column header. (I don't have it in this code because with it the code would not be compiled. I have seen from other code that I need newline or tabularnewline is needed at some place. I don't know the syntax, apparently.)

Third, I am not getting a double vertical bar along the right edge of the table.

\documentclass{amsart}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{makecell}
\usepackage{array}

\begin{document}

\noindent \hspace*{\fill}
\setlength\extrarowheight{2pt}
\begin{tabular}{|| >{\centering\arraybackslash}l |  >{\centering\arraybackslash}p{1.5cm} | >{\centering\arraybackslash}p{2.5cm} | >{\centering\arraybackslash}p{2cm} | >{\centering\arraybackslash}p{2cm} | p{3.5cm} ||} \hline
\multicolumn{5}{|| c ||}{\textbf{Inventory of Clocks and Frequency of Chimes}} \\ \Xhline{0.8pt}
        &   Number of clocks&   Chimes $n$ times on the $n^{\mathrm{th}}$ hour  &   Chimes once on the hour     &   Chimes once on the half-hour \\ \hline
Type A  &   10              &   \checkmark                                      &                               &   \checkmark \\ \hline
Type B  &   5               &   \checkmark                                      &                               &   \\ \hline
Type C  &   3               &                                                   &   \checkmark                  &   \checkmark \\ \hline
\end{tabular}
\hspace{\fill}

\end{document}

Answer 1

\documentclass{amsart}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{makecell}
\usepackage{array}

\begin{document}


\centering
% no, use \centering \noindent \hspace*{\fill}
\setlength\extrarowheight{2pt}
%  >{\centering\arraybackslash}l you can't apply paragraph settings to a `l`
% entry which is one-line.
% you only have 5 columns not 6, so I deleted the last p{}
\begin{tabular}{||l |  >{\centering\arraybackslash}p{1.5cm} | >{\centering\arraybackslash}p{2.5cm} | >{\centering\arraybackslash}p{2cm} | >{\centering\arraybackslash}p{2cm}  ||} \hline
\multicolumn{5}{|| c ||}{\textbf{Inventory of Clocks and Frequency of Chimes}} \\ \Xhline{0.8pt}
        &
\raggedright   Number of clocks&
\raggedright   Chimes $n$ times on the $n^{\mathrm{th}}$ hour  &
\raggedright   Chimes once on the hour     &
\raggedright\arraybackslash   Chimes once on the half-hour \\ \hline
Type A  &   10              &   \checkmark                                      &                               &   \checkmark \\ \hline
Type B  &   5               &   \checkmark                                      &                               &   \\ \hline
Type C  &   3               &                                                   &   \checkmark                  &   \checkmark \\ \hline
\end{tabular}
% no use \centering\hspace{\fill}

\end{document}

Answer 2

Remove the last p column to get the double vertical lines on the right. You are loading makecell package and hence use its \makecell macro to left align the headers. Further, when you use arraybackslash, you can use \\ at the end of row.

\documentclass{amsart}
\usepackage{adjustbox}
\usepackage{mathtools}

\usepackage{makecell}
\usepackage{array}

\begin{document}

\noindent \hspace*{\fill}
\setlength\extrarowheight{2pt}
\begin{tabular}{|| c |  >{\centering\arraybackslash}p{1.5cm} | >{\centering\arraybackslash}p{2.5cm} | >{\centering\arraybackslash}p{2cm} | >{\centering\arraybackslash}p{2cm} ||} \hline
\multicolumn{5}{|| l ||}{\textbf{Inventory of Clocks and Frequency of Chimes}} \\ \Xhline{0.8pt}
        &   \makecell[|l]{Number  \\ of clocks}&   \makecell[|l]{Chimes $n$ times \\ on the $n^{\mathrm{th}}$ hour \\and here}  &   \makecell[|l]{Chimes once \\ on the hour}     &   \makecell[|l]{Chimes once \\ on the \\ half-hour} \\ \hline
Type A  &   10              &   \checkmark                                      &                               &   \checkmark \\ \hline
Type B  &   5               &   \checkmark                                      &                               &   \\ \hline
Type C  &   3               &                                                   &   \checkmark                  &   \checkmark \\ \hline
\end{tabular}
\hspace{\fill}

\end{document}