Explaining, convincing and proving

  • Non-Transitive Dice
    problem
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    Non-transitive dice

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

  • Who's the best?
    problem
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    Who's the best?

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Which countries have the most naturally athletic populations?

  • Always a multiple?
    problem
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    Always a multiple?

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

  • Quadrilaterals in a Square
    problem
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    Quadrilaterals in a square

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    What's special about the area of quadrilaterals drawn in a square?

  • Overlaps
    problem
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    Overlaps

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Can you find ways to put numbers in the overlaps so the rings have equal totals?

  • Garden Shed
    problem
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    Garden shed

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Can you minimise the amount of wood needed to build the roof of my garden shed?

  • Impossibilities
    problem
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    Impossibilities

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Just because a problem is impossible doesn't mean it's difficult...

  • Unequal Averages
    problem
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    Unequal averages

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Play around with sets of five numbers and see what you can discover about different types of average...

  • Reversals
    problem
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    Reversals

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Where should you start, if you want to finish back where you started?

  • Fibonacci Surprises
    problem
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    Fibonacci surprises

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Play around with the Fibonacci sequence and discover some surprising results!