Conjecturing and generalising

  • Polygon Rings
    problem

    Polygon rings

    Age
    11 to 14
    Challenge level
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    Join pentagons together edge to edge. Will they form a ring?

  • Bundles of Cubes
    problem

    Bundles of cubes

    Age
    7 to 11
    Challenge level
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    Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
  • Maxagon
    problem

    Maxagon

    Age
    11 to 14
    Challenge level
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    What's the greatest number of sides a polygon on a dotty grid could have?

  • Regular Hexagon Loops
    problem

    Regular hexagon loops

    Age
    11 to 14
    Challenge level
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    Make some loops out of regular hexagons. What rules can you discover?
  • Last-but-one
    problem

    Last-but-one

    Age
    14 to 16
    Challenge level
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    What is the last-but-one digit of 99! ?
  • Growing Surprises
    problem

    Growing surprises

    Age
    11 to 14
    Challenge level
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    Can you find the connections between linear and quadratic patterns?

  • Square Number Surprises
    problem

    Square number surprises

    Age
    14 to 16
    Challenge level
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    There are unexpected discoveries to be made about square numbers...

  • Multiple Surprises
    problem

    Multiple surprises

    Age
    11 to 16
    Challenge level
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    Sequences of multiples keep cropping up...

  • Fibonacci Surprises
    problem

    Fibonacci surprises

    Age
    11 to 14
    Challenge level
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    Play around with the Fibonacci sequence and discover some surprising results!