Explaining, convincing and proving

  • Product Sudoku
    problem

    Product Sudoku

    Age
    11 to 16
    Challenge level
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    The clues for this Sudoku are the product of the numbers in adjacent squares.

  • Triangle in a Trapezium
    problem

    Triangle in a trapezium

    Age
    11 to 16
    Challenge level
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    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

    Pythagoras proofs

    Age
    11 to 16
    Challenge level
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    Can you make sense of these three proofs of Pythagoras' Theorem?

  • problem

    Shopping basket

    Age
    11 to 16
    Challenge level
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    The items in the shopping basket add and multiply to give the same amount. What could their prices be?

  • Yih or Luk tsut k'i or Three Men's Morris
    game

    Yih or Luk tsut k'i or Three Men's Morris

    Age
    11 to 18
    Challenge level
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    Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.

  • What does it all add up to?
    problem

    What does it all add up to?

    Age
    11 to 18
    Challenge level
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    If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?
  • Russian Cubes
    problem

    Russian cubes

    Age
    14 to 16
    Challenge level
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    I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
  • How old am I?
    problem

    How old am I?

    Age
    14 to 16
    Challenge level
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    In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

  • Chances are
    problem

    Chances are

    Age
    14 to 16
    Challenge level
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    Which of these games would you play to give yourself the best possible chance of winning a prize?

  • problem

    Salinon

    Age
    14 to 16
    Challenge level
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    This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?