Explaining, convincing and proving

  • Mathsland National Lottery
    problem

    Mathsland national lottery

    Age
    14 to 16
    Challenge level
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    Can you work out the probability of winning the Mathsland National Lottery?

  • Fill Me Up Too
    problem

    Fill me up too

    Age
    14 to 16
    Challenge level
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    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?

  • Which list is which?
    problem

    Which list is which?

    Age
    14 to 16
    Challenge level
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    Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

  • The Fastest Cyclist
    problem

    The fastest cyclist

    Age
    14 to 16
    Challenge level
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    Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • Odds and Evens made fair
    problem

    Odds and evens made fair

    Age
    14 to 16
    Challenge level
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    In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

  • Difference of Two Squares
    problem

    Difference of two squares

    Age
    14 to 16
    Challenge level
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    What is special about the difference between squares of numbers adjacent to multiples of three?

  • Pythagoras Perimeters
    problem

    Pythagoras perimeters

    Age
    14 to 16
    Challenge level
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    If you know the perimeter of a right angled triangle, what can you say about the area?

  • Multiplication arithmagons
    problem

    Multiplication arithmagons

    Age
    14 to 16
    Challenge level
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    Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

  • Towering Trapeziums
    problem

    Towering trapeziums

    Age
    14 to 16
    Challenge level
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    Can you find the areas of the trapezia in this sequence?
  • Puzzling Place Value
    problem

    Puzzling place value

    Age
    14 to 16
    Challenge level
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    Can you explain what is going on in these puzzling number tricks?