Working systematically

  • problem

    Fifteen cards

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

    Can you use the information to find out which cards I have used?

  • More children and plants
    problem

    More children and plants

    Age
    7 to 14
    Challenge level
    filled star filled star filled star
    This challenge extends the Plants investigation so now four or more children are involved.
  • Summing Consecutive Numbers
    problem

    Summing consecutive numbers

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

  • Who's the best?
    problem

    Who's the best?

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Which countries have the most naturally athletic populations?

  • Stadium Sightline
    problem

    Stadium sightline

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    How would you design the tiering of seats in a stadium so that all spectators have a good view?

  • A Very Shiny Nose?
    problem

    A very shiny nose?

    Age
    16 to 18
    Challenge level
    filled star filled star empty star

    This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

  • Non-Transitive Dice
    problem

    Non-transitive dice

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

  • Function Pyramids
    problem

    Function pyramids

    Age
    16 to 18
    Challenge level
    filled star empty star empty star

    A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

  • Changing areas, changing volumes
    problem

    Changing areas, changing volumes

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

  • Jumping squares
    problem

    Jumping squares

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.