cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm.
How many of these cubes have no wax of them?

Please, help me, and show me the work. Thanks.



From the wording of your question we are not sure if the wax covers the entire cube of cheese or only part of it. Sue assumed that the wax covers the entire cube. If not then you should be able to modify her argument to find the solution.


Hi liban,

If the wax covers the whole cheese, then it will touch everything on the outside, but none of the inner small cubes. So you need to think: how many inner small cubes are there? Since the whole cheese is four by four by four pieces (as you said, 64 pieces in all), then if you take off a layer on top, bottom, front, back, left and right, you have just two by two by two inner cubes.

Hope this helps!
Stephen La Rocque>