Networks/graph theory

  • Pattern of islands
    problem

    Pattern of islands

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    In how many distinct ways can six islands be joined by bridges so that each island can be reached from every other island...
  • Redblue
    problem

    Redblue

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    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?
  • Fermat's Poser
    problem

    Fermat's poser

    Age
    14 to 16
    Challenge level
    filled star filled star filled star
    Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
  • W Mates
    problem

    W mates

    Age
    16 to 18
    Challenge level
    filled star empty star empty star
    Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
  • Knight Defeated
    problem

    Knight defeated

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    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?
  • Magic W
    problem

    Magic W

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

  • Olympic Magic
    problem

    Olympic magic

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    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?

  • Plum Tree
    problem

    Plum tree

    Age
    14 to 18
    Challenge level
    filled star empty star empty star
    Label this plum tree graph to make it totally magic!
  • Magic Caterpillars
    problem

    Magic caterpillars

    Age
    14 to 18
    Challenge level
    filled star filled star filled star
    Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
  • Instant Insanity
    problem

    Instant insanity

    Age
    11 to 18
    Challenge level
    filled star filled star filled star

    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, that is all 4 colours appear.