Explaining, convincing and proving

  • Multiple Surprises
    problem
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    Multiple Surprises

    Age
    11 to 16
    Challenge level
    1 out of 3

    Sequences of multiples keep cropping up...

  • Same length
    problem
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    Same Length

    Age
    11 to 16
    Challenge level
    2 out of 3

    Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

  • Robotic Rotations
    problem
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    Robotic Rotations

    Age
    11 to 16
    Challenge level
    2 out of 3

    How did the the rotation robot make these patterns?

  • problem
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    Marbles in a Box

    Age
    11 to 16
    Challenge level
    2 out of 3

    How many winning lines can you make in a three-dimensional version of noughts and crosses?

  • Take Three From Five
    problem
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    Take Three From Five

    Age
    11 to 16
    Challenge level
    2 out of 3

    Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

  • Tourism
    problem
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    Tourism

    Age
    11 to 16
    Challenge level
    2 out of 3

    If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

  • Product Sudoku
    problem
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    Product Sudoku

    Age
    11 to 16
    Challenge level
    2 out of 3

    The clues for this Sudoku are the product of the numbers in adjacent squares.

  • Triangle in a Trapezium
    problem
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    Triangle in a Trapezium

    Age
    11 to 16
    Challenge level
    2 out of 3

    Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

  • Pythagoras Proofs
    problem
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    Pythagoras Proofs

    Age
    11 to 16
    Challenge level
    2 out of 3

    Can you make sense of these three proofs of Pythagoras' Theorem?

  • problem
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    Shopping Basket

    Age
    11 to 16
    Challenge level
    3 out of 3

    The items in the shopping basket add and multiply to give the same amount. What could their prices be?