Explaining, convincing and proving

  • Small tomato seedlings in yellow pots.
    problem

    Takeaway Time

    Age
    14 to 16
    Challenge level
    2 out of 3

    Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

  • The Fastest Cyclist
    problem

    The Fastest Cyclist

    Age
    14 to 16
    Challenge level
    2 out of 3

    Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • Small pepper seedlings in turquoise pots.
    problem

    Spot the Fake

    Age
    14 to 16
    Challenge level
    2 out of 3

    One of N coins is slightly heavier than the others. How large can N be if the coin can be determined with only two weighings with a set of scales?

  • Towering Trapeziums
    problem

    Towering Trapeziums

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you find the areas of the trapezia in this sequence?

  • Small pepper seedlings in orange pots.
    problem

    Trolley Park

    Age
    14 to 16
    Challenge level
    2 out of 3

    In a supermarket, there are two lines of tightly packed trolleys. What is the length of one trolley?

  • Small pepper seedlings in turquoise pots.
    problem

    Shaded Square

    Age
    14 to 16
    Challenge level
    2 out of 3

    Weekly Problem 41 - 2016
    The diagram shows a square, with lines drawn from its centre. What is the shaded area?

  • Small tomato seedlings in pink pots.
    problem

    Long List

    Age
    14 to 16
    Challenge level
    2 out of 3

    Weekly Problem 47 - 2017
    How many numbers do I need in a list to have two squares, two primes and two cubes?

  • Small pepper seedlings in turquoise pots.
    problem

    Triangular Intersection

    Age
    14 to 16
    Challenge level
    3 out of 3

    What is the largest number of intersection points that a triangle and a quadrilateral can have?

  • Polycircles
    problem

    Polycircles

    Age
    14 to 16
    Challenge level
    3 out of 3

    Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?