Explaining, convincing and proving

  • Arithmagons
    problem
    Favourite

    Arithmagons

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

    Can you find the values at the vertices when you know the values on the edges?

  • Semi-regular Tessellations
    problem
    Favourite

    Semi-Regular Tessellations

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

    Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

  • problem
    Favourite

    Cyclic Quadrilaterals

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

    Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

  • Statistical shorts
    problem
    Favourite

    Statistical Shorts

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

    Can you decide whether these short statistical statements are always, sometimes or never true?

  • Multiple Surprises
    problem
    Favourite

    Multiple Surprises

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

    Sequences of multiples keep cropping up...

  • Same length
    problem
    Favourite

    Same Length

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

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

  • Robotic Rotations
    problem
    Favourite

    Robotic Rotations

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

    How did the the rotation robot make these patterns?

  • problem
    Favourite

    Marbles in a Box

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

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

  • Take Three From Five
    problem
    Favourite

    Take Three From Five

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

    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
    Favourite

    Tourism

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

    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.