Explaining, convincing and proving

  • Small tomato seedlings in pink pots.
    problem

    Down and Along

    Age
    11 to 14
    Challenge level
    1 out of 3

    Can you work out the values of J, M and C in this sum?

  • Small pepper seedlings in turquoise pots.
    problem

    Other Side

    Age
    11 to 14
    Challenge level
    1 out of 3

    Weekly Problem 8 - 2016
    Can you work out the size of the angles in a quadrilateral?

  • Small pepper seedlings in turquoise pots.
    problem

    Equilateral Pair

    Age
    11 to 14
    Challenge level
    1 out of 3

    Weekly Problem 39 - 2016
    In the diagram, VWX and XYZ are congruent equilateral triangles. What is the size of angle VWY?

  • Small tomato seedlings in pink pots.
    problem

    What's on the Back?

    Age
    11 to 14
    Challenge level
    1 out of 3

    Four cards have a number on one side and a phrase on the back. On each card, the number does not have the property described on the back. What do the four cards have on them?

  • Small pepper seedlings in turquoise pots.
    problem

    Shared Vertex

    Age
    11 to 14
    Challenge level
    1 out of 3

    Weekly Problem 38 - 2017
    In the diagram, what is the value of $x$?

  • Small tomato seedlings in pink pots.
    problem

    Anti-Magic Square

    Age
    11 to 14
    Challenge level
    2 out of 3

    You may have met Magic Squares, now meet an Anti-Magic Square. Its properties are slightly different - can you still solve it?

  • Marbles
    problem

    Marbles

    Age
    11 to 14
    Challenge level
    2 out of 3

    I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

  • Tri-Colour
    problem

    Tri-Colour

    Age
    11 to 14
    Challenge level
    2 out of 3

    Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

  • Aba
    problem

    Aba

    Age
    11 to 14
    Challenge level
    2 out of 3

    In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

  • Even So
    problem

    Even So

    Age
    11 to 14
    Challenge level
    2 out of 3

    Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?