Puzzle of the Week

Each of the two particular vendors is provide a cubical solid wooden object of the same size. Each vendor is asked to cut her cube in the following steps:

Cut the cube fully into N number of smaller cubes so that no waste material is left. Then carve a sphere of the maximum possible size from each smaller cube, thereby obtaining N solid wooden spheres, all of the same size. From all the left over three-dimensional objects carve the maximum possible number of solid wooden spheres of another size, such that all the second set of spheres are the same size too. The only operations allowed are cutting and chiseling. No two objects can be joined together.

All the left over material after obtaining the two sets of spheres is considered to be scrap.

If N for the first vendor is larger than for the second vendor, who will have the smaller volume of total scrap left.


Last date for submitting answers: 25 February 2012