Probably most people will acknowledge the importance of doing exercises when reading a mathematical textbook. Here I am talking about a textbook of similar level as those ones listed in GTM. However, there is usually no solution avalible for those exercises in most mathematical books. When one tries to do exercises without solutions, it seems to me that two problems may occur:
One cannot easily verify if his/her answer is correct. For example, if an exercise asks the reader to find all groups of order $52$, without a solution how can one make sure that s/he has listed all the possible answers without mistake? Even for those "show that" questions, it is still possible that the reader gives a false proof and contains some (possibly non-obvious) errors.
For those questions one just cannot solve after working on it for a long time, how can s/he find out the solution? I know that one can ask the question here or to a teacher or a fellow student, etc.; but is there any better way?
For myself, I find much more motivated to do those exercises with solutions, then compare my answers with the suggested ones, then continue to do more. But for those without solutions I can hardly even motivate myself to attempt them, for the two reasons mentioned above. Anyone has any suggestions on what we should do with those exercises in a textbook?
Any comments and suggestions will be much appreciated.