Conjecturing and generalising

  • Handshakes
    problem

    Handshakes

    Age
    11 to 14
    Challenge level
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    Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
  • Mystic Rose
    problem

    Mystic rose

    Age
    14 to 16
    Challenge level
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    Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

  • Diminishing Returns
    problem

    Diminishing returns

    Age
    11 to 14
    Challenge level
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    How much of the square is coloured blue? How will the pattern continue?

  • The Tower of Hanoi - three wooden poles, with several coloured rings of decreasing sizes on the middle pole.
    problem

    Tower of Hanoi

    Age
    11 to 14
    Challenge level
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    The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

  • Christmas chocolates
    problem

    Christmas chocolates

    Age
    11 to 14
    Challenge level
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    How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

  • How much can we spend?
    problem

    How much can we spend?

    Age
    11 to 14
    Challenge level
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    A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

  • problem

    Cyclic quadrilaterals

    Age
    11 to 16
    Challenge level
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    Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

  • Nice or Nasty
    problem

    Nice or nasty

    Age
    7 to 11
    Challenge level
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    There are nasty versions of this dice game but we'll start with the nice ones...

  • Strike it out
    problem

    Strike it out

    Age
    5 to 11
    Challenge level
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    Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

  • Fix me or crush me
    problem

    Fix me or crush me

    Age
    16 to 18
    Challenge level
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    Can you make matrices which will fix one lucky vector and crush another to zero?