Visualising and representing

  • LOGO Challenge - Triangles-Squares-Stars
    problem

    Logo Challenge - Triangles-Squares-Stars

    Age
    11 to 16
    Challenge level

    Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

  • 11x11 square
    problem

    11×11 Square

    Age
    11 to 16
    Challenge level

    Here's a neat trick you can do with an 11 by 11 square...

  • Yih or Luk tsut k'i or Three Men's Morris
    game

    Yih or Luk Tsut K'i or Three Men's Morris

    Age
    11 to 18
    Challenge level

    Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

  • 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.

  • Placeholder: several colourful numbers
    problem

    Triangles in the Middle

    Age
    11 to 18
    Challenge level
    This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
  • 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.

  • Natural Sum
    problem

    Natural Sum

    Age
    14 to 16
    Challenge level

    The picture illustrates the sum 1 + 2 + 3 + 4 = (4 × 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.

  • Star Gazing
    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?

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