Working systematically

  • Crazy Cannons
    problem

    Crazy Cannons

    Age
    16 to 18
    Challenge level
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    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
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    This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.

  • Spread
    problem

    Spread

    Age
    16 to 18
    Challenge level
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    Given the mean and standard deviation of a set of marks, what is the greatest number of candidates who could have scored 100%?

  • Towards Maclaurin
    problem

    Towards Maclaurin

    Age
    16 to 18
    Challenge level
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    Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

  • Interpolating polynomials
    problem

    Interpolating Polynomials

    Age
    16 to 18
    Challenge level
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    Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
  • Latin Squares
    article

    Latin Squares

    A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
  • Maths Trails
    article

    Maths Trails

    The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.