Vertical strikethrough

Question

I'm currently trying to TeX up a Sieve of Eratosthenes example on the integers 2-100. I'm already using the ulem and cancel packages to give me horizontal and diagonal strikethroughs but I need a vertical strikethrough as well which would go through the same point as the horizontal and diagonal strikethroughs.

It doesn't have to be a general solution so one that works for 2-digit numbers in math-mode will suffice.

\documentclass[pdf]{beamer}
\usepackage{ulem}
\usepackage{cancel}
\newcommand{\strike}[1]{\text{\sout{$#1$}}}
\begin{document}
\begin{array}{c c c c c c c c c c}
    & \cancel{2\:} & \strike{3\:} & \cancel{4\:} & \bcancel{5\:} & \strike{\cancel{6\:}} & 7\: & \cancel{8\:} & \strike{9\:} & \xcancel{10}\\
    11 & \strike{\cancel{12}} & 13 & \cancel{14} & \bcancel{\strike{15}} & \cancel{16} & 17 & \strike{\cancel{18}} & 19 & \xcancel{20}\\
    \strike{21} & \cancel{22} & 23 & \strike{\cancel{24}} & \bcancel{25} & \cancel{26} & \strike{27} & \cancel{28} & 29 & \strike{\xcancel{30}}\\
    31 & \cancel{32} & \strike{33} & \cancel{34} & \bcancel{\textcolor{red}{35}} & \strike{\cancel{36}} & 37 & \cancel{38} & \strike{39} & \xcancel{40}\\
    41 & \strike{\cancel{42}} & 43 & \cancel{44} & \bcancel{\strike{45}} & \cancel{46} & 47 & \strike{\cancel{48}} & 49 & \xcancel{50}\\
    \strike{51} & \cancel{52} & 53 & \strike{\cancel{54}} & \bcancel{55} & \cancel{56} & \strike{57} & \cancel{58} & 59 & \strike{\xcancel{60}}\\
    61 & \cancel{62} & \strike{63} & \cancel{64} & \bcancel{65} & \strike{\cancel{66}} & 67 & \cancel{68} & \strike{69} & \xcancel{\textcolor{red}{70}}\\
    71 & \strike{\cancel{72}} & 73 & \cancel{74} & \bcancel{\strike{75}} & \cancel{76} & 77 & \strike{\cancel{78}} & 79 & \xcancel{80}\\
    \strike{81} & \cancel{82} & 83 & \strike{\cancel{84}} & \bcancel{85} & \cancel{86} & \strike{87} & \cancel{88} & 89 & \strike{\xcancel{90}}\\
    91 & \cancel{92} & 93 & \cancel{94} & \bcancel{95} & \strike{\cancel{96}} & 97 & \cancel{98} & \strike{99} & \xcancel{100}\\
\end{array}
\end{document}

What I'd like to do is add horizontal strikes to the multiples of 7 now but can't seem to do it nicely. I've tried using something like

\newcommand{\hstrike}[1]{\strike{#1}\!\mid}

or

\newcommand{\hstrike}[1]{| \! \strike{#1}}

But it screws up the rest of the formatting and that's not changed if I use \mkern instead of \!.

Answer 1

I created \vstrike{} and used in on "7" and "93". I also redefined all your cancel routines to make them of uniform rule thickness and length, and going through the same intersection point.

EDITED to demonstrate the Full Monty on "101".

\documentclass[pdf]{beamer}
\usepackage{stackengine,graphicx}
\def\stacktype{L}
\def\useanchorwidth{T}
%\usepackage{ulem}
\newcommand\xcancel[1]{\bcancel{\cancel{#1}}}
\newcommand\bcancel[1]{\stackon[7pt]{#1}{\rotatebox{-30}{\rule{2.9ex}{1pt}}}}
\newcommand\cancel[1]{\stackon[0pt]{#1}{\rotatebox{30}{\rule{2.9ex}{1pt}}}}
\newcommand\strike[1]{\stackon[3.3pt]{#1}{\rule{2.9ex}{1pt}}}
\newcommand\vstrike[1]{\stackon{#1}{\smash{\rule[-3pt]{1pt}{2.9ex}}}}
\begin{document}
\[
\begin{array}{c c c c c c c c c c}
    & \cancel{2} & \strike{3} & \cancel{4} & \bcancel{5} & \strike{\cancel{6}} & \vstrike{7}\: & \cancel{8} & \strike{9} & \xcancel{10}\\
    11 & \strike{\cancel{12}} & 13 & \cancel{14} & \bcancel{\strike{15}} & \cancel{16} & 17 & \strike{\cancel{18}} & 19 & \xcancel{20}\\
    \strike{21} & \cancel{22} & 23 & \strike{\cancel{24}} & \bcancel{25} & \cancel{26} & \strike{27} & \cancel{28} & 29 & \strike{\xcancel{30}}\\
    31 & \cancel{32} & \strike{33} & \cancel{34} & \bcancel{\textcolor{red}{35}} & \strike{\cancel{36}} & 37 & \cancel{38} & \strike{39} & \xcancel{40}\\
    41 & \strike{\cancel{42}} & 43 & \cancel{44} & \bcancel{\strike{45}} & \cancel{46} & 47 & \strike{\cancel{48}} & 49 & \xcancel{50}\\
    \strike{51} & \cancel{52} & 53 & \strike{\cancel{54}} & \bcancel{55} & \cancel{56} & \strike{57} & \cancel{58} & 59 & \strike{\xcancel{60}}\\
    61 & \cancel{62} & \strike{63} & \cancel{64} & \bcancel{65} & \strike{\cancel{66}} & 67 & \cancel{68} & \strike{69} & \xcancel{\textcolor{red}{70}}\\
    71 & \strike{\cancel{72}} & 73 & \cancel{74} & \bcancel{\strike{75}} & \cancel{76} & 77 & \strike{\cancel{78}} & 79 & \xcancel{80}\\
    \strike{81} & \cancel{82} & 83 & \strike{\cancel{84}} & \bcancel{85} & \cancel{86} & \strike{87} & \cancel{88} & 89 & \strike{\xcancel{90}}\\
    91 & \cancel{92} & \vstrike{93} & \cancel{94} & \bcancel{95} & \strike{\cancel{96}} & 97 & \cancel{98} & \strike{99} & \xcancel{100}\\
\strike{\vstrike{\xcancel{101}}}
\end{array}
\]
\end{document}