Exploring and noticing

  • Pair Sums
    problem

    Pair sums

    Age
    11 to 14
    Challenge level
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    Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

  • 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?

  • Top-Heavy Pyramids
    problem

    Top-heavy pyramids

    Age
    11 to 14
    Challenge level
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    Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.
  • 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
    Favourite

    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
    Favourite

    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
    Favourite

    Diamond collector

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