Explaining, convincing and proving

  • Convex Polygons
    problem

    Convex Polygons

    Age
    11 to 14
    Challenge level

    Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

  • More Total Totality
    problem

    More Total Totality

    Age
    11 to 14
    Challenge level

    Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?

  • Distinct in a Line
    problem

    Distinct in a Line

    Age
    11 to 14
    Challenge level

    This grid can be filled so that each of the numbers 1, 2, 3, 4, 5 appears just once in each row, column and diagonal. Which number goes in the centre square?

  • Small pepper seedlings in orange pots.
    problem

    Knights and Knaves

    Age
    11 to 14
    Challenge level

    Knights always tell the truth. Knaves always lie. Can you catch these knights and knaves out?

  • Small pepper seedlings in orange pots.
    problem

    To Run or Not to Run?

    Age
    11 to 14
    Challenge level

    If an athlete takes 10 minutes longer to walk, run and cycle three miles than he does to cycle all three miles, how long does it take him?

  • More Number Sandwiches
    problem

    More Number Sandwiches

    Age
    11 to 16
    Challenge level

    When is it impossible to make number sandwiches?

  • The Triangle Game
    game

    The Triangle Game

    Age
    11 to 16
    Challenge level

    Can you discover whether this is a fair game?

  • Classifying Solids using Angle Deficiency
    problem

    Classifying Solids Using Angle Deficiency

    Age
    11 to 16
    Challenge level

    Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

  • Where are the primes?
    problem

    Where Are the Primes?

    Age
    11 to 16
    Challenge level

    What can we say about all the primes which are greater than 3?

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