Exploring and noticing

  • 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.

  • Follow the numbers
    problem

    Follow the numbers

    Age
    7 to 11
    Challenge level
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    What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

  • More pebbles
    problem

    More pebbles

    Age
    7 to 11
    Challenge level
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    Have a go at this 3D extension to the Pebbles problem.
  • Charlie's delightful machine
    problem

    Charlie's delightful machine

    Age
    11 to 16
    Challenge level
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    Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

  • A little light thinking
    problem

    A little light thinking

    Age
    14 to 16
    Challenge level
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    Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

  • Four Coloured Lights
    problem

    Four coloured lights

    Age
    11 to 14
    Challenge level
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    Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?
  • Guessing the graph
    problem

    Guessing the graph

    Age
    14 to 16
    Challenge level
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    Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?