Visualising and representing

  • Troublesome Dice
    problem

    Troublesome Dice

    Age
    11 to 14
    Challenge level
    1 out of 3
    When dice land edge-up, we usually roll again. But what if we didn't...?
  • Small pepper seedlings in orange pots.
    problem

    Starting Fibonacci

    Age
    11 to 14
    Challenge level
    1 out of 3

    What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

  • Small pepper seedlings in turquoise pots.
    problem

    Painted Octahedron

    Age
    11 to 14
    Challenge level
    1 out of 3

    What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?

  • Small pepper seedlings in turquoise pots.
    problem

    Squares in a Square

    Age
    11 to 14
    Challenge level
    1 out of 3

    In the diagram, the small squares are all the same size. What fraction of the large square is shaded?

  • Small pepper seedlings in turquoise pots.
    problem

    Soma Surface

    Age
    11 to 14
    Challenge level
    1 out of 3

    What is the surface area of the solid shown?

  • Cube Paths
    problem

    Cube Paths

    Age
    11 to 14
    Challenge level
    2 out of 3

    Given a 2 by 2 by 2 skeletal cube with one route 'down' the cube. How many routes are there from A to B?

  • Triangular Tantaliser
    problem

    Triangular Tantaliser

    Age
    11 to 14
    Challenge level
    2 out of 3

    Draw all the possible distinct triangles on a 4 × 4 dotty grid. Convince me that you have all possible triangles.

  • Flight of the Flibbins
    problem

    Flight of the Flibbins

    Age
    11 to 14
    Challenge level
    2 out of 3

    Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?

  • Königsberg
    problem

    Königsberg

    Age
    11 to 14
    Challenge level
    2 out of 3

    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?

  • Clocked
    problem

    Clocked

    Age
    11 to 14
    Challenge level
    2 out of 3

    Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?