Exploring and noticing

  • Differences
    problem
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    Differences

    Age
    11 to 14
    Challenge level
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    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

  • One to Eight
    problem
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    One to Eight

    Age
    11 to 14
    Challenge level
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    Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

  • How Many Miles To Go?
    problem
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    How Many Miles to Go?

    Age
    11 to 14
    Challenge level
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    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?

  • Up and across
    problem
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    Up and Across

    Age
    11 to 14
    Challenge level
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    Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

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

    Age
    11 to 14
    Challenge level
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    Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

  • A Chance to Win?
    problem
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    A Chance to Win?

    Age
    11 to 14
    Challenge level
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    Imagine you were given the chance to win some money... and imagine you had nothing to lose...

  • Going to the cinema
    problem
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    Going to the Cinema

    Age
    11 to 16

    A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

  • Diamond Collector
    game
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    Diamond Collector

    Age
    11 to 16
    Challenge level
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    Collect as many diamonds as you can by drawing three straight lines.

  • What's it worth?
    problem
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    What's It Worth?

    Age
    11 to 16
    Challenge level
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    There are lots of different methods to find out what the shapes are worth - how many can you find?

  • Square It
    problem
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    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.