Exploring and noticing

  • What does random look like?
    problem

    What does random look like?

    Age
    11 to 14
    Challenge level
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    Engage in a little mathematical detective work to see if you can spot the fakes.

  • problem

    Inky cube

    Age
    7 to 14
    Challenge level
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    This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

  • 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?

  • Sitting round the party tables
    problem

    Sitting round the party tables

    Age
    5 to 11
    Challenge level
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    Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

  • 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?

  • Your number was...
    problem

    Your number was...

    Age
    11 to 14
    Challenge level
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    Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

  • Ip Dip
    problem

    Ip dip

    Age
    5 to 11
    Challenge level
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    "Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

  • Newspaper Sheets
    problem

    Newspaper sheets

    Age
    14 to 16
    Challenge level
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    From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?
  • Almost Constant Digits
    problem

    Almost constant digits

    Age
    11 to 14
    Challenge level
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    How many 10-digit numbers containing only 1s, 2s and 3s can you write?
  • Triple Cubes
    problem

    Triple cubes

    Age
    5 to 11
    Challenge level
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    This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.