Explaining, convincing and proving

  • Three consecutive odd numbers
    problem

    Three Consecutive Odd Numbers

    Age
    11 to 16
    Challenge level

    How many sets of three consecutive odd numbers can you find, in which all three numbers are prime?

  • Adding odd numbers
    problem

    Adding Odd Numbers

    Age
    11 to 16
    Challenge level

    Is there a quick and easy way to calculate the sum of the first 100 odd numbers?

  • Cyclic Quadrilaterals Proof
    problem

    Cyclic Quadrilaterals Proof

    Age
    11 to 16
    Challenge level

    Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?

  • Subtended angles
    problem

    Circumference Angles

    Age
    11 to 16
    Challenge level

    Can you prove the angle properties described by some of the circle theorems?

  • 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

    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.

  • The Bridges of Konigsberg
    problem

    The Bridges of Konigsberg

    Age
    11 to 18
    Challenge level

    Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

  • What does it all add up to?
    problem

    What Does It All Add Up To?

    Age
    11 to 18
    Challenge level

    If you take four consecutive numbers and add them together, the answer will always be even. What else do you notice?

  • Doodles
    problem

    Doodles

    Age
    14 to 16
    Challenge level

    Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?

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