Reasoning, convincing and proving

  • All Change
    problem

    All change

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

    There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

  • Patterns of inflection
    problem

    Patterns of inflection

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

    Find the relationship between the locations of points of inflection, maxima and minima of functions.

  • 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?

  • Olympic Records
    problem

    Olympic records

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

    Can you deduce which Olympic athletics events are represented by the graphs?

  • problem

    Who's the winner?

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

    When two closely matched teams play each other, what is the most likely result?

  • 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?

  • Generating Triples
    problem

    Generating triples

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

    Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

  • Seriesly
    problem

    Seriesly

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

    Prove that k.k! = (k+1)! - k! and sum the series 1.1! + 2.2! + 3.3! +...+n.n!

  • Fill Me Up Too
    problem

    Fill me up too

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

    In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?