\relax 
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
\global\let\oldcontentsline\contentsline
\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
\global\let\oldnewlabel\newlabel
\gdef\newlabel#1#2{\newlabelxx{#1}#2}
\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
\AtEndDocument{\ifx\hyper@anchor\@undefined
\let\contentsline\oldcontentsline
\let\newlabel\oldnewlabel
\fi}
\fi}
\global\let\hyper@last\relax 
\gdef\HyperFirstAtBeginDocument#1{#1}
\providecommand*\HyPL@Entry[1]{}
\citation{wiki}
\HyPL@Entry{0<</S/D>>}
\citation{UN}
\citation{BK}
\citation{B}
\citation{rowsums}
\@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}{section.1}}
\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces Example of a small puzzle}}{2}{table.1}}
\newlabel{1example}{{1}{2}{Example of a small puzzle}{table.1}{}}
\citation{M}
\citation{M}
\citation{M}
\citation{BZconf}
\newlabel{mullenFormula}{{1}{3}{}{theorem.1}{}}
\newlabel{eq11}{{1}{3}{}{equation.1.1}{}}
\citation{B}
\citation{B}
\citation{M}
\citation{M}
\@writefile{toc}{\contentsline {section}{\numberline {2}The main result}{4}{section.2}}
\newlabel{main}{{2}{4}{The main result}{section.2}{}}
\newlabel{mainTheorem}{{2}{4}{}{theorem.2}{}}
\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces The probability of being useless for some small $n$}}{4}{table.2}}
\newlabel{G_n_table}{{2}{4}{The probability of being useless for some small $n$}{table.2}{}}
\citation{M}
\citation{M}
\citation{M}
\citation{M}
\@writefile{toc}{\contentsline {section}{\numberline {3}Proof of Theorem\nobreakspace  {}\ref  {mainTheorem}}{5}{section.3}}
\newlabel{the-proof}{{3}{5}{Proof of Theorem~\ref {mainTheorem}}{section.3}{}}
\newlabel{amk}{{3}{5}{Proof of Theorem~\ref {mainTheorem}}{equation.3.3}{}}
\newlabel{G_n}{{4}{5}{Proof of Theorem~\ref {mainTheorem}}{equation.3.4}{}}
\newlabel{prop}{{3}{5}{}{theorem.3}{}}
\newlabel{eq1}{{5}{6}{Proof of Theorem~\ref {mainTheorem}}{equation.3.5}{}}
\newlabel{phi_lemma}{{4}{6}{}{theorem.4}{}}
\newlabel{eq2}{{6}{6}{}{equation.3.6}{}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Conclusion of the proof of Theorem\nobreakspace  {}\ref  {mainTheorem}}{6}{subsection.3.1}}
\newlabel{eqa}{{8}{7}{Conclusion of the proof of Theorem~\ref {mainTheorem}}{equation.3.8}{}}
\newlabel{fin1}{{9}{7}{Conclusion of the proof of Theorem~\ref {mainTheorem}}{equation.3.9}{}}
\newlabel{fin2}{{10}{7}{Conclusion of the proof of Theorem~\ref {mainTheorem}}{equation.3.10}{}}
\citation{M}
\citation{BSW}
\@writefile{toc}{\contentsline {section}{\numberline {4}Does the sequence $nG_n / F_{n+2}$ converge?}{8}{section.4}}
\newlabel{new}{{4}{8}{Does the sequence $nG_n / F_{n+2}$ converge?}{section.4}{}}
\citation{BG}
\citation{BSW}
\newlabel{neweq}{{11}{9}{Does the sequence $nG_n / F_{n+2}$ converge?}{equation.4.11}{}}
\newlabel{neweq1}{{12}{9}{Does the sequence $nG_n / F_{n+2}$ converge?}{equation.4.12}{}}
\bibcite{BG}{1}
\bibcite{BK}{2}
\bibcite{rowsums}{3}
\bibcite{B}{4}
\bibcite{BZconf}{5}
\bibcite{BSW}{6}
\bibcite{M}{7}
\bibcite{UN}{8}
\bibcite{wiki}{9}