"I would like to know what all the possible solutions are for each problem." ... I'm sure you would, I'm sure we'd all love to know all the solutions to any problem, but that ain't practical. Yes, I know this is student writing.
And don't, for the love of all that's sane, don't ask for the "best" solution to a problem. The goodness of a solution depends on the environment the problem is in; many things make one solution better than another given a different context.
What you should do is consider some solutions and if nothing seems to work, then ask "I like solution A but it needs input B which is very difficult for me. Solution C is a way around this limitation, but doesn't look as effective due to D. what can you guys suggest ?"
"Wir hoffen, dass dieses Mal alles gut gehen wird!"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.