Conjecturing and generalising

  • Garden Shed
    problem
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    Garden Shed

    Age
    11 to 14
    Challenge level
    2 out of 3

    Can you minimise the amount of wood needed to build the roof of my garden shed?

  • Unequal Averages
    problem
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    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...

  • Fibonacci Surprises
    problem
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    Fibonacci Surprises

    Age
    11 to 14
    Challenge level
    2 out of 3

    Play around with the Fibonacci sequence and discover some surprising results!

  • Terminating or not
    problem
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    Terminating or Not

    Age
    11 to 14
    Challenge level
    2 out of 3

    Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?

  • What numbers can we make now?
    problem
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    What Numbers Can We Make Now?

    Age
    11 to 14
    Challenge level
    2 out of 3

    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

  • Differences
    problem
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    Differences

    Age
    11 to 14
    Challenge level
    3 out of 3

    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

  • 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?

  • 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...

  • 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?