OCR MEI D1 2005 June — Question 2

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2005
SessionJune
TopicGraph Theory Fundamentals

2 Answer this question on the insert provided. A maze is constructed by building east/west and north/south walls so that there is a route from the entrance to the exit. The maze is shown in Fig. 2.1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{03df7d9e-63d4-48fb-9cf3-e92003f44788-3_495_717_470_671} \captionsetup{labelformat=empty} \caption{Fig. 2.1}
\end{figure} On entering the maze Janet says "I'm always going to keep a hand in contact with the wall on the right." John says "I'm always going to keep a hand in contact with the wall on the left."
  1. On the insert for this question show Janet's route through the maze. On the insert show John's route.
  2. Will these strategies always find a way through such mazes? Justify your answer. In some mazes the objective is to get to a marked point before exiting. An example is shown in Fig. 2.2, where \(\mathbf { X }\) is the marked point. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{03df7d9e-63d4-48fb-9cf3-e92003f44788-3_497_716_1672_669} \captionsetup{labelformat=empty} \caption{Fig. 2.2}
    \end{figure} In the maze shown in Fig. 2.2 Janet's algorithm takes her to \(\mathbf { X }\). John's algorithm does not take him to \(\mathbf { X }\). John modifies his algorithm by saying that he will turn his back on the exit if he arrives there without visiting \(\mathbf { X }\). He will then move onwards, continuing to keep a hand in contact with the wall on the left.
  3. Will this modified algorithm take John to the point \(\mathbf { X }\) in the maze in Fig. 2.2?
  4. Will this modified algorithm take John to any marked point in the maze in Fig. 2.2? Justify your answer.