I have a set of 120 items from which I need to form 30 groups of 4 items.
But there are items in the 120 that should not wind up in the same group. I don’t know how to calculate how trivial or impossible it is to satisfy that condition.
How many random rules of the form “Item #X cannot be grouped with Item #Y” can I tolerate before it starts to become difficult to do the grouping?
I realize there are pathological rule combinations, like if one item is unpairable with every single other item. My interest is more in having some idea if having 10 random such rules gets iffy, or is it 100 or 1000 or a million or a billion rules or what? Not sure where to even start to get some sense of this.
Any advice would be greatly appreciated, thanks!!