Explaining, convincing and proving

  • Speeding boats
    problem
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    Speeding Boats

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

    Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

  • Partly Painted Cube
    problem
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    Partly Painted Cube

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

    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

  • Mathsland National Lottery
    problem
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    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
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    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?

  • Which list is which?
    problem
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    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?

  • Odds and Evens made fair
    problem
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    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
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    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
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    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
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    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?

  • Puzzling Place Value
    problem
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    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?