Reasoning, convincing and proving

  • Mathsland National Lottery
    problem

    Mathsland national lottery

    Age
    14 to 16
    Challenge level
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    Can you work out the probability of winning the Mathsland National Lottery?

  • problem

    Pairs of numbers

    Age
    5 to 7
    Challenge level
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    If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

  • Do you feel lucky?
    problem

    Do you feel lucky?

    Age
    11 to 14
    Challenge level
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    Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

  • Last one standing
    problem

    Last one standing

    Age
    14 to 16
    Challenge level
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    Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

  • Sociable Cards
    problem

    Sociable cards

    Age
    11 to 14
    Challenge level
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    Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

  • Curious number
    problem

    Curious number

    Age
    7 to 11
    Challenge level
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    Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

  • Takeaway Time
    problem

    Takeaway time

    Age
    14 to 16
    Challenge level
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    Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?
  • Hiking the Hill
    problem

    Hiking the hill

    Age
    14 to 16
    Challenge level
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    Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?
  • Kept Apart
    problem

    Kept apart

    Age
    11 to 14
    Challenge level
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    The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?
  • Inner equality
    problem

    Inner equality

    Age
    16 to 18
    Challenge level
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    Can you solve this inequalities challenge?