Reasoning, convincing and proving

  • Russian Cubes
    problem

    Russian cubes

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

    Doodles

    Age
    14 to 16
    Challenge level
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    Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
  • Be reasonable
    problem

    Be reasonable

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.
  • Fixing It
    problem

    Fixing it

    Age
    16 to 18
    Challenge level
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    A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?
  • Building with Solid Shapes
    problem

    Building with solid shapes

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

  • Chain of Changes
    problem

    Chain of changes

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it?

  • A City of Towers
    problem

    A city of towers

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

  • Colouring Triangles
    problem

    Colouring triangles

    Age
    5 to 7
    Challenge level
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    Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

  • problem

    Noah

    Age
    5 to 7
    Challenge level
    filled star filled star empty star

    Noah saw 12 legs walk by into the Ark. How many creatures did he see?

  • Let's Investigate Triangles
    problem

    Let's investigate triangles

    Age
    5 to 7
    Challenge level
    filled star empty star empty star

    Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?