Conjecturing and generalising

  • Six Ten Total
    problem

    Six ten total

    Age
    7 to 11
    Challenge level
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    This challenge combines addition, multiplication, perseverance and even proof.

  • Multiplication arithmagons
    problem

    Multiplication arithmagons

    Age
    14 to 16
    Challenge level
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    Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

  • Beach Huts
    problem

    Beach huts

    Age
    11 to 14
    Challenge level
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    Can you figure out how sequences of beach huts are generated?

  • Unequal Averages
    problem

    Unequal averages

    Age
    11 to 14
    Challenge level
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    Play around with sets of five numbers and see what you can discover about different types of average...

  • Wipeout
    problem

    Wipeout

    Age
    11 to 16
    Challenge level
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    Can you do a little mathematical detective work to figure out which number has been wiped out?

  • About Average
    problem

    About average

    Age
    11 to 14
    Challenge level
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    Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?

  • Hollow Squares
    problem

    Hollow squares

    Age
    14 to 16
    Challenge level
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    Which armies can be arranged in hollow square fighting formations?

  • Difference of Two Squares
    problem

    Difference of two squares

    Age
    14 to 16
    Challenge level
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    What is special about the difference between squares of numbers adjacent to multiples of three?

  • Garden Shed
    problem

    Garden shed

    Age
    11 to 14
    Challenge level
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    Can you minimise the amount of wood needed to build the roof of my garden shed?

  • Forwards Add Backwards
    problem

    Forwards add backwards

    Age
    11 to 14
    Challenge level
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    What happens when you add a three digit number to its reverse?