Conjecturing and generalising

  • Arithmagons
    problem

    Arithmagons

    Age
    11 to 16
    Challenge level
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    Can you find the values at the vertices when you know the values on the edges?

  • Stars
    problem

    Stars

    Age
    11 to 14
    Challenge level
    filled star filled star empty star
    Can you work out what step size to take to ensure you visit all the dots on the circle?
  • Square It
    problem

    Square it

    Age
    11 to 16
    Challenge level
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    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

  • Hundred Square Poster
    problem

    Hundred square

    Age
    5 to 11
    Challenge level
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    A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

  • Can it be?
    problem

    Can it be?

    Age
    16 to 18
    Challenge level
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    When if ever do you get the right answer if you add two fractions by adding the numerators and adding the denominators?
  • Lots of Lollies
    problem

    Lots of lollies

    Age
    5 to 7
    Challenge level
    filled star filled star filled star

    Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

  • Share Bears
    problem

    Share bears

    Age
    5 to 7
    Challenge level
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    Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?
  • Shadow Play
    problem

    Shadow play

    Age
    5 to 7
    Challenge level
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    Here are shadows of some 3D shapes. What shapes could have made them?

  • The Bridges of Konigsberg
    problem

    The bridges of Konigsberg

    Age
    11 to 18
    Challenge level
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    Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

  • Tourism
    problem

    Tourism

    Age
    11 to 14
    Challenge level
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    If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.