Homework assignments have two purposes: they will help you learn the material and strengthen your ability to solve problems, and they will provide training in writing mathematics.
Regarding the first part, the main issue of importance is that you end up understanding how to solve the problems. You will of course learn the most if you manage to solve all the problems on your own, so you are encouraged to start with giving this your best try. If some problems are not overcome in this way, then you will also learn a lot by discussing them with other students. Get together in groups and see if you can solve the problems together. You could also ask for hints from me or Sriram or anyone else who is willing to help you. If all these efforts do not result in a solution, then it is still much better to learn and understand a solution than not understanding one, so in this situation you are encouraged to learn a solution in any way you can. For example, you can search the web, read books, ask somebody (e.g. me or Sriram) to explain how to solve a problem, or even read other students' solutions.
On the other hand, the write-ups must be individual. Once you understand your solution, then you close your web browser and sit down to write up your solution clearly and correctly in your own words. If you have received help, then cite your sources (e.g. "I learned this solution from user xyz at mathoverflow.net"). You should think about your solution as an essay with rigorous mathematical content. In particular, you should explain what you do and write neatly in grammatically correct sentences. Do not write more than necessary, but include enough information that somebody at approximately your own level can easily understand your solution. It is also very useful to consider if any steps in your solution could be done simpler, this might cut down on the writing and make the final product even easier to read. These expository efforts will help you build the skills you need for writing an excellent thesis and research papers.
Good luck!
Anders