Networks/graph theory

  • Redblue
    problem

    Redblue

    Age
    7 to 11
    Challenge level
    Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?
  • Hamilton's Puzzle
    problem

    Hamilton's Puzzle

    Age
    7 to 11
    Challenge level
    I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?
  • Placeholder: several colourful numbers
    problem

    Round-Robin Scheduling

    Age
    7 to 14
    Challenge level

    Think about the mathematics of round robin scheduling.

  • Pattern of islands
    problem

    Pattern of Islands

    Age
    11 to 14
    Challenge level

    In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...

  • Königsberg
    problem

    Königsberg

    Age
    11 to 14
    Challenge level

    Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

  • Classifying Solids using Angle Deficiency
    problem

    Classifying Solids Using Angle Deficiency

    Age
    11 to 16
    Challenge level

    Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

  • The Bridges of Konigsberg
    problem

    The Bridges of Konigsberg

    Age
    11 to 18
    Challenge level

    Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

  • Four coloured wooden cubes balanced precariously to make a tower.
    problem

    Instant Insanity

    Age
    11 to 18
    Challenge level

    Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated.

  • Knight Defeated
    problem

    Knight Defeated

    Age
    14 to 16
    Challenge level

    The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board for any value of n. How many ways can a knight do this on a 3 by 4 board?

  • Olympic Magic
    problem

    Olympic Magic

    Age
    14 to 16
    Challenge level

    in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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