Combinations

  • 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?
  • Break it up!
    problem

    Break it up!

    Age
    5 to 11
    Challenge level
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    In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

  • Train Carriages
    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?
  • problem

    Teddy Town

    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?

  • Five Coins
    problem

    Five coins

    Age
    5 to 11
    Challenge level
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    Ben has five coins in his pocket. How much money might he have?

  • Three by Three
    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?

  • problem

    The puzzling sweet shop

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

    There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p in the sweet shop. What could each of the children buy with their money?

  • 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
    filled star filled star empty star

    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?