Cubes and cuboids

  • Solids
    problem

    Solids

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

    A task which depends on members of the group working collaboratively to reach a single goal.

  • problem

    Marbles in a box

    Age
    11 to 16
    Challenge level
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    How many winning lines can you make in a three-dimensional version of noughts and crosses?

  • Nine Colours
    problem

    Nine colours

    Age
    11 to 16
    Challenge level
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    Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

  • Instant Insanity
    game

    Instant insanity

    Age
    11 to 18
    Challenge level
    filled star empty star empty star
    We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.
  • Geometry and Measure - Short Problems
    problem

    Which face?

    Age
    14 to 16
    Challenge level
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    Which faces are opposite each other when this net is folded into a cube?

  • Three cubes
    problem

    Three cubes

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

    Can you work out the dimensions of the three cubes?

  • Painted Cube
    problem

    Painted cube

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

    Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

  • The Spider and the Fly
    problem

    The spider and the fly

    Age
    14 to 16
    Challenge level
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    A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

  • Summing squares
    problem

    Summing squares

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  • Partly Painted Cube
    problem

    Partly painted cube

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

    Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?