Any problem can be transformed into many different contradictions. Consider, for example, the problem of inaccuracy of the traditional method of evaluating the amount of the waste water discussed in the article "Improving Lift/Pump Stations Using TRIZ" by Abram Teplitskiy, Igor Endovtsev and Roustem Kourmaev published in the May 2007 issue of the TRIZ-journal.
The authors transformed it into the following contradiction: there might be inflow of the waste water during emptying the collection container AND there should be no inflow in order to accurately measure the amount of wastewater contributed by a client. But influx of the waste water during pumping it out is not the only factor that makes the system in question inaccurate. Another factor is the speed of pumping out. Were the pump able to empty the collection container momentarily, the influx of the waste water would not matter. The system would be absolutely accurate regardless of whether there is influx or not. Thus, the same problem can be converted into the following contradiction: the pump has to have the infinite speed of pumping and cannot have the infinite speed of pumping.
This contradiction might be much more difficult to resolve. But benefits of its solution could be much greater than those of resolving the contradiction that Abram Teplitskiy et al were focusing upon. Making speed of pumping infinite and finite at the same time could lead to many break-through.
So, what contradiction to pursue ? This is already the question of trials and errors. But TRIZ rejects the trials and errors approach to problem solving. It develops the means of their reduction. But surprisingly these very means while supposedly eliminating the need in one kind of trials definitely require the other one. Specifically, instead of "what if I do this" type of trials TRIZ introduces "what if I try to resolve this contradiction" type of trials. And who knows which type is better ? Moreover, we have a third type of trials here: either conduct the first one or the second !
But does it make any difference which type of trials to conduct - the old one condemned by TRIZ or the new one introduced by TRIZ ? As one noticed, "it ain't the choices we make; it's what's inside of us that makes us turn out the way we are" - either good problem solvers or not.