partitioning - Find all possible partitions of n elements with k-sized subsets, where two elements share same set only once -

I have n elements that need to be divided into x sets, each set has exactly k = 4 elements.

I need to find all the possible divisions with the hindrance that each pair element shares only one set once.

So if I [1 2 3 4] [5 6 7 8] [...] can not hold all consecutive divisions eg [X 2 X] or [x x 1] set Are unarmed.

Turn off this problem however, they solve the problem only for arbitrary size sets.

Example: I have 32 rats that can be placed in 8 cages, 4 in each cage. Mice should be rotated between cages in a fashion that they never meet another mouse twice. How often can you do this and what are the configurations?

This is an example of "social golfer." There was a page (page) with a group of solutions to different problem sizes in Warwick Harvey, but it appears that in your case 10 answers are rotated, but I do not know what the actual configuration is. Here is the 9-rotation solution, though:

This is an unsolved problem for normal N and.