Visualising and representing

  • Small pepper seedlings in turquoise pots.
    problem

    Semicircular Design

    Age
    14 to 16
    Challenge level

    Weekly Problem 9 - 2016
    The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

  • Quadratic Matching
    problem

    Quadratic Matching

    Age
    14 to 16
    Challenge level

    Can you match each graph to one of the statements?

  • Wari
    game

    Wari

    Age
    14 to 16
    Challenge level
    This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
  • Just Opposite
    problem

    Just Opposite

    Age
    14 to 16
    Challenge level
    A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
  • Building Tetrahedra
    problem

    Building Tetrahedra

    Age
    14 to 16
    Challenge level

    Can you make a tetrahedron whose faces all have the same perimeter?

  • Contact
    problem

    Contact

    Age
    14 to 16
    Challenge level
    A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
  • Proximity
    problem

    Proximity

    Age
    14 to 16
    Challenge level

    We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

  • One and three
    problem

    One and Three

    Age
    14 to 16
    Challenge level

    Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

  • Gnomon dimensions
    problem

    Gnomon Dimensions

    Age
    14 to 16
    Challenge level
    These gnomons appear to have more than a passing connection with the Fibonacci sequence. This problem ask you to investigate some of these connections.
  • Overlap
    problem

    Overlap

    Age
    14 to 16
    Challenge level

    A red square and a blue square overlap. Is the area of the overlap always the same?

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