Trial and Improvement

I'm starting to think this may be the way to get students to tackle those questions that they leave blank because they can't remember what to do.

Having studied at an OU summer school I was astonished how many students there used Trial and Improvement to answer the maths problems we were given. This was across the board including geometric, algebraic and trigonometric problems. I have also found that when asking adults to help me gain evidence for my OU maths education assignments they also use Trial and Improvement to tackle the questions I present them with.

The next question is which kind of questions can be answered using Trial and Improvement?
Can all questions be answered in this way?
Can students adapt the method to answer very different types of question?

The idea is that the student guesses the answer then computes if that answer leads to a correct conclusion. If it does they are finished but if not they have to use some sort of understanding to guess again and thus get closer to the correct solution. I'm not sure how many of the GCSE questions can be answered by this technique and I'm not sure how successful pupils will be using it but it is perhaps the one technique they can learn that will enable them to answer the questions they usually leave blank and thus gain no marks for.

I'll have to do more work on this to see how widely it can be applied.