Explaining, convincing and proving

  • Pythagorean Fibs
    problem

    Pythagorean Fibs

    Age
    16 to 18
    Challenge level
    2 out of 3

    What have Fibonacci numbers got to do with Pythagorean triples?

  • Integral Sandwich
    problem

    Integral Sandwich

    Age
    16 to 18
    Challenge level
    2 out of 3

    Generalise this inequality involving integrals.

  • Impossible square?
    problem

    Impossible Square?

    Age
    16 to 18
    Challenge level
    2 out of 3

    Can you make a square from these triangles?

  • Impossible triangles?
    problem

    Impossible Triangles?

    Age
    16 to 18
    Challenge level
    2 out of 3

    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
    2 out of 3

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

  • Farey Neighbours
    problem

    Farey Neighbours

    Age
    16 to 18
    Challenge level
    2 out of 3

    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
    2 out of 3

    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
    2 out of 3

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

  • Inverting Rational Functions
    problem

    Inverting Rational Functions

    Age
    16 to 18
    Challenge level
    2 out of 3

    Consider these questions concerning inverting rational functions

  • Top marks
    problem

    Top Marks

    Age
    16 to 18
    Challenge level
    2 out of 3

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