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2024-04-02 21:15:34 -07:00
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commit c10ef06d85
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Advanced/De Bruijn/parts/0 intro.tex
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@ -3,7 +3,7 @@
\example{}<lockproblem>
A certain electronic lock has two buttons: \texttt{0} and \texttt{1}.
It opens as soon as the correct two-digit code is entered, completely ignoring
previous inputs.\hspace{-0.5ex}\footnotemark{} For example, if the correct code is \text{10}, the lock will open
previous inputs. For example, if the correct code is \text{10}, the lock will open
once the sequence \texttt{010} is entered.
\vspace{2mm}
@ -19,36 +19,38 @@ Unlock this lock with only 5 keypresses.
\begin{solution}
The sequence \texttt{00110} is guaranteed to unlock this lock.
\end{solution}
\vfill
Now, consider the same lock, now set with a three-digit binary code.
\problem{}
How many codes are possible?
\vfill
\problem{}
Consider the same lock, now set with a three-digit binary code.
\begin{itemize}
\item How many codes are possible?
\item What is the shortest sequence that is guaranteed to unlock the lock? \par
\hint{You'll need 10 digits.}
\end{itemize}
Show that there is no solution with fewer than three keypresses
\vfill
\problem{}
What is the shortest sequence that is guaranteed to unlock the lock? \par
\hint{You'll need 10 digits.}
\begin{solution}
\begin{itemize}
\item $2^3 = 8$
\item \texttt{0001110100} will do.
\end{itemize}
\texttt{0001110100} will do.
\end{solution}
\problem{}
How about a four-digit code? How many digits do we need? \par
\begin{instructornote}
Don't spend too much time here.
Provide a solution at the board once everyone has had a few
minutes to think about this problem.
\end{instructornote}
\begin{solution}
One example is \texttt{0000 1111 0110 0101 000}
\end{solution}
%\problem{}
%How about a four-digit code? How many digits do we need? \par
%
%\begin{instructornote}
% Don't spend too much time here.
% Provide a solution at the board once everyone has had a few
% minutes to think about this problem.
%\end{instructornote}
%
%\begin{solution}
% One example is \texttt{0000 1111 0110 0101 000}
%\end{solution}
\vfill
\pagebreak