How to deal with exercises with no solutions given? 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.
 A: I think that it would be nice to have a separate book with full workout solutions.
Remember that sometime there is more than one choice to get to the right answer.However the person that is making use of this book will have the option to choose the best way he understands the most and that he or she can easily remember.
I think that every one should be mature enough not to cheat on himself,and use such a book as a tool to check his abilities.
A: For exercises with solutions, there is a terrible bias : you work much less to find the solution.
The thing is that you don't really need to find the solution of an exercise, a good exercise should let you think a lot of the profound nature of the problem.
The exercises without solutions are the best to learn, by far. 
And after some days, if you still don't find the solution and you are frustrated, ask a fellow. It encourages discussion which is really good for learning.
Your problem $\#1$ is a fake problem, because at the end when you write a proof, you know if there is something that is not perfectly clear in your proof. Once you've learnt how to write a perfect detailed proof, there is no space for mistakes.
