Working systematically

  • Thinking Mathematically - Short Problems
    problem

    AP Train

    Age
    16 to 18
    Challenge level
    1 out of 3

    An arithmetic progression is shifted and shortened, but its sum remains the same...

  • Archimedes Numerical Roots
    problem

    Archimedes Numerical Roots

    Age
    16 to 18
    Challenge level
    1 out of 3

    How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

  • The right volume
    problem

    The Right Volume

    Age
    16 to 18
    Challenge level
    1 out of 3

    Can you rotate a curve to make a volume of 1?

  • Function Pyramids
    problem

    Function Pyramids

    Age
    16 to 18
    Challenge level
    1 out of 3

    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?

  • The Koch Snowflake
    problem

    The Koch Snowflake

    Age
    16 to 18
    Challenge level
    1 out of 3

    Explore the strange geometrical properties of the Koch Snowflake.

  • Ante Up
    problem

    Ante Up

    Age
    16 to 18
    Challenge level
    2 out of 3

    Use cunning to work out a strategy to win this game.

  • Max throw
    problem

    Max Throw

    Age
    16 to 18
    Challenge level
    2 out of 3

    At what angle should you throw something to maximise the distance it travels?

  • Crazy Cannons
    problem

    Crazy Cannons

    Age
    16 to 18
    Challenge level
    2 out of 3

    Two cannons are fired at one another and the cannonballs collide... what can you deduce?

  • A Very Shiny Nose?
    problem

    A Very Shiny Nose?

    Age
    16 to 18
    Challenge level
    2 out of 3

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

  • How fast does it grow?
    problem

    How Fast Does It Grow?

    Age
    16 to 18
    Challenge level
    3 out of 3

    Exponential functions grow pretty quickly...