Free will is one of the easiest hard questions, as millennia-old philosophical dilemmas go. Yudkowsky has suggested that aspiring reductionists should try to solve it on their own in advance of reading the LessWrong analysis.

Non-spoiler posts

The following posts can be read to set up the problem of "free will" and what constitutes a good solution from a reductionist perspective, without entirely giving away the solution. (When Yudkowsky wrote these posts, he thought he could get away with just leaving it as a practice problem, and some of the posts state that the problem will be left open. However Yudkowsky did eventually find that he needed to write out the whole solution.)

How An Algorithm Feels From Inside (see also the wiki page)
Dissolving the Question - this is where the "free will" puzzle is explicitly posed, along with criteria for what does and does not constitute a satisfying answer.
Wrong Questions
Righting a Wrong Question

For spoiler posts see free will (solution).