Visualising and representing

  • Small pepper seedlings in orange pots.
    problem

    Printing Error

    Age
    11 to 14
    Challenge level

    Every third page number in this book has been omitted. Can you work out what number will be on the last page?

  • Troublesome Dice
    problem

    Troublesome Dice

    Age
    11 to 14
    Challenge level
    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

    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

    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

    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

    What is the surface area of the solid shown?

  • Is there a theorem?
    problem

    Is There a Theorem?

    Age
    11 to 14
    Challenge level

    Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

  • Cube Paths
    problem

    Cube Paths

    Age
    11 to 14
    Challenge level

    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

    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

    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?

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