Combinations

  • Two and One
    problem

    Two and One

    Age
    5 to 7
    Challenge level
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    Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

  • Four-Triangle Arrangements
    problem

    Four-Triangle Arrangements

    Age
    5 to 7
    Challenge level
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    How many different shapes can you make by putting four right- angled isosceles triangles together?
  • A blue train carriage against a blue sky.
    problem

    Train Carriages

    Age
    5 to 11
    Challenge level
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    Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

  • Coloured counters on a white background. One green counter is surrounded by six blue counters.
    problem

    Three by Three

    Age
    5 to 11
    Challenge level
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    Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column

  • Three Way Mix Up
    problem

    Three Way Mix Up

    Age
    5 to 11
    Challenge level
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    Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

  • Two on Five
    problem

    Two on Five

    Age
    5 to 11
    Challenge level
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    Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

  • problem

    Teddy Town - Part Two

    Age
    5 to 11
    Challenge level
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    There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

  • problem

    Teddy Town - Part Three

    Age
    5 to 11
    Challenge level
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    There are sixteen teddies in Teddy Town - four red, four blue, four yellow and four green. There are also sixteen houses, four of each colour. Can you put them on the map of Teddy Town according to the rules?

  • problem

    Teddy Town - Part Four

    Age
    5 to 11
    Challenge level
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    There are twenty five teddies in Teddy Town - five red, five blue, five yellow, five green and five purple. There are also twenty five houses, five of each colour. Can you put them on the map of Teddy Town according to the rules?

  • problem

    Teddy Town - Part Five

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

    There are thirty six teddies in Teddy Town - six red, six blue, six yellow, six green, six purple and six turquoise. There are also thirty six houses, six of each colour. Can you put them on the map of Teddy Town according to the rules?