Visualising and representing

  • Convex Polygons
    problem

    Convex polygons

    Age
    11 to 14
    Challenge level
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    Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
  • Three by One
    problem

    Three by one

    Age
    16 to 18
    Challenge level
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    There are many different methods to solve this geometrical problem - how many can you find?

  • Hexy-Metry
    problem

    Hexy-metry

    Age
    14 to 16
    Challenge level
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    A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

  • Corridors
    problem

    Corridors

    Age
    14 to 16
    Challenge level
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    A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
  • Counters
    problem

    Counters

    Age
    7 to 11
    Challenge level
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    Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
  • Make 37 Poster
    problem

    Make 37

    Age
    5 to 11
    Challenge level
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    Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

  • Königsberg
    problem

    Königsberg

    Age
    11 to 14
    Challenge level
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    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?

  • Shady Symmetry
    problem

    Shady symmetry

    Age
    11 to 14
    Challenge level
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    How many different symmetrical shapes can you make by shading triangles or squares?

  • Pick's Theorem
    problem

    Pick's theorem

    Age
    14 to 16
    Challenge level
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    Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

  • Take Three From Five
    problem

    Take three from five

    Age
    11 to 16
    Challenge level
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    Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?