Call a set of cubes incongruent if they all have different side lengths. Prove that it is impossible to exactly fill a rectangular box with incongruent cubes.

Note: The phrase "exactly fill" means that there is no space in the box which is not occupied by a cube, and that the cubes themselves should be packed together to form the shape of the rectangular box that envelops them.

Posted

Call a set of cubes incongruent if they all have different side lengths. Prove that it is impossible to exactly fill a rectangular box with incongruent cubes.

Note: The phrase "exactly fill" means that there is no space in the box which is not occupied by a cube, and that the cubes themselves should be packed together to form the shape of the rectangular box that envelops them.

## Share this post

## Link to post

## Share on other sites