Two methods invented by the author are presented here which help in some common cases of difficulty in solving problems. The first is called ‘The method of description’. It is suitable for the case where the solver has become thoroughly stuck with a given problem and no idea seems to come to mind. The second is suitable for the case where the solver has been trapped in a loop and goes in circles round the problem. The methods are each presented in two forms; one strict and one more ‘humanized’. The former is suitable for making a computer model as well, where the model incorporating the methods solves difficult problems. The fact that the methods can become a computer program constitutes a rigorous test for them. Some analysis of these difficulties is also attempted here.