Many problems can be characterized by a set of tuples (action, the possibility of the action, property of object undergoing the action, the possibility of the property, result, its wantedness). For example, consider the following problem situation. To obtain a wanted result R when action A1 is excerted on an object it has to have property P1, but to obtain a wanted result when action A2 is excerted the object has to have property P2. This situation can be characterized by 2 tuples: (A1, possible, P1, possible, R, wanted) and (A2, possible, P2, possible, R, wanted). The problem is due to object cannot have two properties P1 and P2 at the same time.
Consider another situation: to convert an object with a property P1 into an object with property P it has to be underwent action A1, which is impossible. But in order for a possible action A2 converted an object into object with property P it has to have initial property P2. Here we have 2 tuples: (A1, impossible, P1, possible, R, wanted) and (A2, possible, P2, possible, R, wanted).
Generally, the number of actions involved in a situation could be not 2 but greater. The same goes for the number of object properties and the number of results. Thus, one additional tuple charaterizes a situation. This tuple is (I, J, K, L, M, N), where I is the number of actions, J is the number of impossible actions, K is the number of object properties, L is the number of impossible properties, M is the total number of results, N is the number of unwanted results. In what follows I will call such an additional tuple the characteristic tuple of a problem situation.
The first situation above is characterized by the following additonal tuple (2, 0, 2, 0, 2, 0), whereas the second situation is characterized by an additional tuple (2, 1, 2, 0, 2, 0).
The situation contains a contradicrtion when either J>0, or K>1, or N>0. The both aforementioned situations contain a contradiction.
Here are other possible problem situations containing a contradiction.
We considered problem situations characterized by tuples
(2, 0, 2, 0, 2, 0)
(2, 1, 2, 0, 2, 0)
(1, 0, 2, 0, 2, 1)
(2, 0, 1, 0, 3, 1)
(1, 1, 1, 0, 1, 0)
(2, 0, 2, 1, 2, 1)
Generally, the number of different actions and object properties can hardly be greater than 2, whereas the number of results could be as high as 4. Thus all problem situations can be characterized by 2 x 3 x 2 x 3 x 4 x 5 = 720 different characteristic tuples. Hence, there are 720 types of problem situations and corresponding physical/logical contradictions.