AQA D1 2006 January — Question 7

Exam BoardAQA
ModuleD1 (Decision Mathematics 1)
Year2006
SessionJanuary
TopicRoute Inspection

7 Stella is visiting Tijuana on a day trip. The diagram shows the lengths, in metres, of the roads near the bus station.
\includegraphics[max width=\textwidth, alt={}, center]{4a186c87-5f84-4ec3-8cc3-a0ed8721b040-06_1539_1162_495_424} Stella leaves the bus station at \(A\). She decides to walk along all of the roads at least once before returning to \(A\).
  1. Explain why it is not possible to start from \(A\), travel along each road only once and return to \(A\).
  2. Find the length of an optimal 'Chinese postman' route around the network, starting and finishing at \(A\).
  3. At each of the 9 places \(B , C , \ldots , J\), there is a statue. Find the number of times that Stella will pass a statue if she follows her optimal route.