Cubes and cuboids

  • Sugary Diversion
    problem

    Sugary diversion

    Age
    11 to 14
    Challenge level
    filled star empty star empty star
    Weekly Problem 48 - 2008
    An ant is crawling in a straight line when he bumps into a one centimetre cube of sugar.If he climbs over it before before continuing on his intended route, how much does the detour add to the length of his journey?
  • Drilling many cubes
    problem

    Drilling many cubes

    Age
    7 to 14
    Challenge level
    filled star filled star empty star
    A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.
  • Start Cube Drilling
    problem

    Start cube drilling

    Age
    5 to 7
    Challenge level
    filled star filled star filled star
    Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
  • Painted Faces
    problem

    Painted faces

    Age
    7 to 11
    Challenge level
    filled star empty star empty star
    Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
  • Cube Drilling
    problem

    Cube drilling

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?
  • Twelve Cubed
    problem

    Twelve cubed

    Age
    14 to 16
    Challenge level
    filled star empty star empty star
    A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?
  • Interpenetrating solids
    problem

    Interpenetrating solids

    Age
    16 to 18
    Challenge level
    filled star filled star empty star
    This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!
  • Cheese cutting
    problem

    Cheese cutting

    Age
    16 to 18
    Challenge level
    filled star filled star filled star
    In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
  • Noughts and crosses
    problem

    Noughts and crosses

    Age
    11 to 14
    Challenge level
    filled star filled star filled star
    Ever thought of playing three dimensional Noughts and Crosses? This problem might help you visualise what's involved.
  • Cubic Covering
    problem

    Cubic covering

    Age
    14 to 16
    Challenge level
    filled star filled star empty star
    A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?