Working systematically

  • Linked Chains
    problem

    Linked chains

    Age
    7 to 11
    Challenge level
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    Can you find ways to make twenty-link chains from these smaller chains? This gives opportunities for different approaches.

  • Fraction Lengths
    problem

    Fraction lengths

    Age
    7 to 11
    Challenge level
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    Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?

  • Open Squares
    problem

    Open squares

    Age
    7 to 11
    Challenge level
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    This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

  • Painting Possibilities
    problem

    Painting possibilities

    Age
    7 to 11
    Challenge level
    filled star filled star filled star

    This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes and the small cubes that would fit inside each one.

  • Dart Target
    problem

    Dart target

    Age
    7 to 11
    Challenge level
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    This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

  • Matching Criminals
    problem

    Matching criminals

    Age
    14 to 18
    Challenge level
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    DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.

  • The ELISA Test
    problem

    The ELISA test

    Age
    14 to 18
    Challenge level
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    In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

  • Who's who?
    problem

    Who's who?

    Age
    11 to 16
    Challenge level
    filled star filled star empty star

    Can you solve the clues to find out who's who on the friendship graph?

  • Dice Stairs
    problem

    Dice stairs

    Age
    7 to 11
    Challenge level
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    Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?