Conjecturing and generalising

  • Enclosing Squares
    problem
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    Enclosing Squares

    Age
    11 to 14
    Challenge level
    3 out of 3

    Can you find sets of sloping lines that enclose a square?

  • How Many Miles To Go?
    problem
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    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?

  • Cubes within Cubes revisited
    problem
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    Cubes Within Cubes Revisited

    Age
    11 to 14
    Challenge level
    3 out of 3

    Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

  • Litov's Mean Value Theorem
    problem
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    Litov's Mean Value Theorem

    Age
    11 to 14
    Challenge level
    3 out of 3

    Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

  • Cunning Card Trick
    problem
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    Cunning Card Trick

    Age
    11 to 14
    Challenge level
    3 out of 3

    Delight your friends with this cunning trick! Can you explain how it works?

  • Consecutive negative numbers
    problem
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    Consecutive Negative Numbers

    Age
    11 to 14
    Challenge level
    3 out of 3

    Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

  • Square It
    problem
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    Square It

    Age
    11 to 16
    Challenge level
    1 out of 3

    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.

  • Arithmagons
    problem
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    Arithmagons

    Age
    11 to 16
    Challenge level
    1 out of 3

    Can you find the values at the vertices when you know the values on the edges?

  • problem
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    Cyclic Quadrilaterals

    Age
    11 to 16
    Challenge level
    1 out of 3

    Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?