Explaining, convincing and proving

  • Pythagorean Fibs
    problem

    Pythagorean Fibs

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

    What have Fibonacci numbers got to do with Pythagorean triples?

  • Integral Sandwich
    problem

    Integral Sandwich

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

    Generalise this inequality involving integrals.

  • Impossible square?
    problem

    Impossible Square?

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

    Can you make a square from these triangles?

  • Impossible triangles?
    problem

    Impossible Triangles?

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

    Which of these triangular jigsaws are impossible to finish?

  • Mind your \Ps and \Qs
    problem

    Mind Your Ps and Qs

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

    Sort these mathematical propositions into a series of 8 correct statements.

  • Farey Neighbours
    problem

    Farey Neighbours

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

    Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?

  • The clue is in the question
    problem

    The Clue Is in the Question

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

    Starting with one of the mini-challenges, how many of the other mini-challenges will you invent for yourself?

  • Matrix meaning
    problem

    Matrix Meaning

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

    Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

  • Top marks
    problem

    Top Marks

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

    Can you make all of these statements about averages true at the same time?