I have a 3-dimensional cuboid, with dimensions 2x2x1. I wish to divide this into smaller EQUAL sized cuboids of size 2x1x1. Then I want to extend this case for larger cuboids, assuming that equal smaller cuboids are possible. What are the possible number of ways to do this? I thought of this logic, but I don't think it is correct.
We will have a cuboid of volume 4, have to divide this into 2 cuboids of volume 2. Possible options are 2!, (choose any 1 dimension in which I keep the 2 as it is, and divide the other one) However I feel that this logic is incorrect, especially when I go for cases like 2x2x2 or 2x2x4 or even larger.
Any help would be appreciated.