It's simple enough of a proposal. Make a page where we post open problems, work on solutions to said problems, and where we can discuss these problems prior to attempting to solve them with other LWers. I would suggest two main parts:

1. Lesswrong specific/original problems, i.e., problems posed by LWers, or which are particularly relevant to LW style rationality.
2. General problems which we believe LWers should have the tools to solve, but which have not been solved.

I would propose using the same karma system we use now. Each problem could have a long list of proposed solutions, cautionary comments, and newly found lemmas relevant to the problem, and each solution, warning, or lemma, could have its own comment tree section. But it is important that we don't think of solutions as articles; they should be scientific writing. No sentence or phrase should be in a solution without adding to the literal meaning of the solution. We should judge solutions based on how well they solve the problem, not on how well written they are. We might even want to make chat rooms devoted to each problem, so that we can actively engage in conversation in stead of waiting for comment responses. 

This would have at least three major benefits:

1. We would have a place for LW students to actually practice their skills on fresh problems without putting them through the less effective torture of already solved, homework-like tasks.
2. We would have a large record of our successes and failures as rationalists, and an easy way to get a sense of how far we've come since 2011.
3. This would provide us with a way to test the results of LW style rationality training/study by looking at who has been giving the best solutions. If we find that after a few years of being on LW, 50% of LWers give a really good solution to one of the open problems, then we can conclude that reading/using LW has had positive effects on the rationality of its readers/users.