Visualising and representing

  • The night sky with stars above some tree silhouettes.
    problem

    Star Gazing

    Age
    14 to 16
    Challenge level

    Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

  • Five coloured cubes forming the edges of a pentagon.
    problem

    Penta Colour

    Age
    14 to 16
    Challenge level

    In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?

  • Two changing rooms in a clothes shop.
    problem

    Changing Places

    Age
    14 to 16
    Challenge level

    Place a red counter in the top left corner of a 4×4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

  • Small pepper seedlings in turquoise pots.
    problem

    Out of the Window

    Age
    14 to 16
    Challenge level

    Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

  • Triangles within Triangles
    problem

    Triangles Within Triangles

    Age
    14 to 16
    Challenge level

    Can you find a rule which connects consecutive triangular numbers?

  • Small pepper seedlings in turquoise pots.
    problem

    Rectangle Rearrangement

    Age
    14 to 16
    Challenge level

    A 3×8 rectangle is cut into two pieces... then rearranged to form a right-angled triangle. What is the perimeter of the triangle formed?

  • Small pepper seedlings in turquoise pots.
    problem

    Twelve Cubed

    Age
    14 to 16
    Challenge level

    A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

  • Small pepper seedlings in turquoise pots.
    problem

    Dicey Directions

    Age
    14 to 16
    Challenge level

    An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

  • The perforated cube
    problem

    The Perforated Cube

    Age
    14 to 16
    Challenge level

    A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

  • Efficient packing
    problem

    Efficient Packing

    Age
    14 to 16
    Challenge level

    How efficiently can you pack together disks?

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