Three minipages next to eachother and aligned to top

Question

I am trying to put 3 minipages right next to each other, but since the text for n=8 is so wide, it is going to the next line. How would I fix this so that they are all side by side, and they all align "topwise", so that the n=6, n=7 and n=8 are all on the same line? Here is the latex code

\begin{figure}[h]
    \centering
\begin{minipage}{.3\textwidth}
    \centering
   \begin{flalign} 
   &\textrm{\underline{$n=6$}} \nonumber \\
   &000000111111 \nonumber \\
   &010100101011 \nonumber \\
   &010000101111 \nonumber \\
   &0011 \nonumber \\
   &001000110111 \nonumber \\
   &000100111011 \nonumber 
   \end{flalign}   
\end{minipage}%
\begin{minipage}{0.3\textwidth}
    \centering 
\begin{flalign}
   &\textrm{\underline{$n=7$}} \nonumber \\
   &00000001111111 \nonumber \\
   &01 \nonumber \\
   &01010001010111 \nonumber \\
   &01000001011111 \nonumber \\
   &00110001100111 \nonumber \\
   &00101001101011 \nonumber \\
   &00100001101111 \nonumber \\
   &00010001110111 \nonumber \\
   &00001001111011 \nonumber \\
   &01001001011011 \nonumber 
\end{flalign}
\end{minipage}%

\begin{minipage}{0.3\textwidth}
    \centering
    \begin{flalign}
   &\textrm{\underline{$n=8$}} \nonumber \\
   &0000000011111111 \nonumber \\
   &0101010010101011 \nonumber \\
   &0101000010101111 \nonumber \\
   &0100100010110111 \nonumber \\
   &0100000010111111 \nonumber \\
   &0011100011000111 \nonumber \\
   &0011010011001011 \nonumber \\
   &0011000011001111 \nonumber \\
   &0010100011010111 \nonumber \\
   &0010000011011111 \nonumber \\
   &0001010011101011 \nonumber \\
   &0001000011101111 \nonumber \\
   &0000100011110111 \nonumber \\
   &0000010011111011 \nonumber \\
   &0100010010111011 \nonumber \\
   &0010010011011011 \nonumber 
   \end{flalign}

    \end{minipage}
    \label{fig:prob3}
    \caption{Decomposition of Huang's de Bruijn sequence}
\end{figure}

Answer 1

There was an error and 3 omissions. The error was a blank line after the second minpage which inserted therefore a paragraph break. The omission was the [t] optional argument on all 3 minipages to get top alignment.

\documentclass{article}
%\usepackage[margin=5.5cm]{geometry}
\usepackage{amsmath}
\begin{document}
\begin{figure}[h]
    \centering
\begin{minipage}[t]{.3\textwidth}
    \centering
   \begin{flalign} 
   &\textrm{\underline{$n=6$}} \nonumber \\
   &000000111111 \nonumber \\
   &010100101011 \nonumber \\
   &010000101111 \nonumber \\
   &0011 \nonumber \\
   &001000110111 \nonumber \\
   &000100111011 \nonumber 
   \end{flalign}   
\end{minipage}%
\begin{minipage}[t]{0.3\textwidth}
    \centering 
\begin{flalign}
   &\textrm{\underline{$n=7$}} \nonumber \\
   &00000001111111 \nonumber \\
   &01 \nonumber \\
   &01010001010111 \nonumber \\
   &01000001011111 \nonumber \\
   &00110001100111 \nonumber \\
   &00101001101011 \nonumber \\
   &00100001101111 \nonumber \\
   &00010001110111 \nonumber \\
   &00001001111011 \nonumber \\
   &01001001011011 \nonumber 
\end{flalign}
\end{minipage}%
\begin{minipage}[t]{0.3\textwidth}
    \centering
    \begin{flalign}
   &\textrm{\underline{$n=8$}} \nonumber \\
   &0000000011111111 \nonumber \\
   &0101010010101011 \nonumber \\
   &0101000010101111 \nonumber \\
   &0100100010110111 \nonumber \\
   &0100000010111111 \nonumber \\
   &0011100011000111 \nonumber \\
   &0011010011001011 \nonumber \\
   &0011000011001111 \nonumber \\
   &0010100011010111 \nonumber \\
   &0010000011011111 \nonumber \\
   &0001010011101011 \nonumber \\
   &0001000011101111 \nonumber \\
   &0000100011110111 \nonumber \\
   &0000010011111011 \nonumber \\
   &0100010010111011 \nonumber \\
   &0010010011011011 \nonumber 
   \end{flalign}

    \end{minipage}
    \label{fig:prob3}
    \caption{Decomposition of Huang's de Bruijn sequence}
\end{figure}
\end{document}