Combinations

  • problem

    Teddy Town - part five

    Age
    5 to 11
    Challenge level
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    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?

  • problem

    Teddy Town - part four

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

    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 three

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

    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 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?

  • Five More Coins
    problem

    Five more coins

    Age
    7 to 11
    Challenge level
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    Could Ben have any amount of money between 5p and £2 in his pocket if he has five coins?
  • Fruity Pairs
    problem

    Fruity pairs

    Age
    5 to 7
    Challenge level
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    Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

  • Unequal Exam
    problem

    Unequal exam

    Age
    11 to 14
    Challenge level
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    120 students sit an exam with 100 marks available. What is the smallest number of pairs that are awarded the same mark?
  • Nine or Ten?
    problem

    Nine or ten?

    Age
    11 to 14
    Challenge level
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    Is a score of 9 more likely than a score of 10 when you roll three dice?
  • Polydron
    problem

    Polydron

    Age
    7 to 11
    Challenge level
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    This activity investigates how you might make squares and pentominoes from Polydron.
  • Placeholder: several colourful numbers
    article

    Binomial coefficients

    An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.