Lesson 3D.3.1

3D.3.1 The route inspection (Chinese postman) algorithm Quiz: Pearson Edexcel Further Maths, Unit 37

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 3D.3.1, The route inspection (Chinese postman) algorithm: 20 multiple choice questions for the Pearson Edexcel Further Maths (9FM0), Unit 37: Algorithms on graphs II, written with Revision Ninja.

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The 20 questions

  1. What is the primary objective of the route inspection problem?

    • Visit all vertices once
    • Traverse all edges minimally
    • Find shortest single path
    • Minimise maximum edge weight

  2. In this specification, what is the most odd vertices a route inspection network can contain?

    • four
    • six
    • two
    • eight

  3. What is the minimum route inspection length for an Eulerian network?

    • Double edge weight
    • Zero
    • Maximum edge weight
    • Total edge weight

  4. How are odd vertices dealt with in a route inspection problem?

    • Single edges
    • Longest paths
    • Paired shortest paths
    • Random paths

  5. What must every vertex degree become after adding repeated edges in route inspection?

    • Odd degree
    • Zero degree
    • Even degree
    • Prime degree

  6. What type of vertex does a route inspection tour start and end at?

    • A dead end
    • An odd vertex
    • Different vertices
    • The same vertex

  7. How many ways are there to pair up 4 odd vertices?

    • 3
    • 8
    • 4
    • 6

  8. A network has exactly two odd vertices, and the shortest path between them has length 3. The total weight of all edges is 20. What is the minimum route inspection length?

    • 17
    • 26
    • 20
    • 23

  9. Four odd vertices A, B, C and D have shortest path lengths AB 2, CD 3, AC 5, BD 4, AD 6 and BC 7. What is the minimum total length of the repeated paths?

    • 5
    • 13
    • 3
    • 9

  10. A network has total edge weight 30. Its odd vertices can be paired with repeats totalling 5. What is the minimum route length?

    • 25
    • 40
    • 35
    • 30

  11. A network is Eulerian with total edge weight 18. What is the minimum route inspection length?

    • 9
    • 18
    • 36
    • 20

  12. A network with four odd vertices has pairing totals 7, 9 and 11, and total edge weight 25. What is the minimum route length?

    • 36
    • 30
    • 34
    • 32

  13. A network has total edge weight 44, and the shortest repeats needed to pair its odd vertices total 7. What is the minimum route length?

    • 56
    • 47
    • 37
    • 51

  14. Odd vertices P, Q, R and S have pair distances PQ 4, RS 4, PR 10, QS 10, PS 3 and QR 2. What is the minimum total repeat length?

    • 20
    • 3
    • 8
    • 5

  15. A route inspection on a network of total weight 42 has length 50. What repeat length was needed?

    • 8
    • 42
    • 92
    • 50

  16. Four odd vertices P, Q, R and S have pair distances PQ 3, RS 3, PR 6, QS 2, PS 4 and QR 5. What is the minimum total repeat length?

    • 5
    • 9
    • 8
    • 6

  17. How must odd vertices be connected during a route inspection algorithm?

    • In sequence
    • In pairs
    • In isolation
    • Using single edges

  18. What two conditions make an augmented network Eulerian?

    • Even degrees and connected
    • Odd degrees and connected
    • Even degrees and directed
    • All weights equal

  19. A network has total weight 60 and a minimum pairing repeat of 12. The route must start and end at A. What is its length?

    • 84
    • 72
    • 48
    • 60

  20. A postman's route must start and end at the same vertex. The network has total weight 45 and the minimum repeats total 10. What is the route length?

    • 50
    • 55
    • 65
    • 45

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