Working systematically

  • Opposite vertices
    problem
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    Opposite Vertices

    Age
    11 to 14
    Challenge level
    2 out of 3

    Can you recreate squares and rhombuses if you are only given a side or a diagonal?

  • A blue patchwork quilt draped over a white sofa.
    problem
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    Alison's Quilt

    Age
    11 to 14
    Challenge level
    2 out of 3

    Nine squares are fitted together to form a rectangle. Can you find its dimensions?

  • Changing areas, changing volumes
    problem
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    Changing Areas, Changing Volumes

    Age
    11 to 14
    Challenge level
    2 out of 3

    How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

  • Non-Transitive Dice
    problem
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    Non-Transitive Dice

    Age
    11 to 14
    Challenge level
    2 out of 3

    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
    Favourite

    Who's the Best?

    Age
    11 to 14
    Challenge level
    2 out of 3

    Which countries have the most naturally athletic populations?

  • Overlaps
    problem
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    Overlaps

    Age
    11 to 14
    Challenge level
    2 out of 3

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

  • Unequal Averages
    problem
    Favourite

    Unequal Averages

    Age
    11 to 14
    Challenge level
    2 out of 3

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

  • Four playing cards on top of each other. Each card shows a different ace.
    problem
    Favourite

    Snappy Statements

    Age
    11 to 14
    Challenge level
    2 out of 3

    Use properties of numbers to work out whether you can satisfy all these statements at the same time.

  • Triangles to Tetrahedra
    problem
    Favourite

    Triangles to Tetrahedra

    Age
    11 to 14
    Challenge level
    3 out of 3

    Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

  • How Many Miles To Go?
    problem
    Favourite

    How Many Miles to Go?

    Age
    11 to 14
    Challenge level
    3 out of 3

    How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?