Steve_Rayhawk comments on Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 113 - Less Wrong Discussion
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Pessimistic assumption: There are more than two endings. A solution meeting the stated criteria is a necessary but not sufficient condition for the least sad ending.
Note that the referent of "Ch. 121" is not necessarily fixed in advance.
Counterargument: "I expect that the collective effect of 'everyone with more urgent life issues stays out of the effort' shifts the probabilities very little" suggests that reasonable prior odds of getting each ending are all close to 0 or 1, so any possible hidden difficulty thresholds are either very high or very low.
Counterargument: The challenge in Three Worlds Collide only had two endings.
Counterargument: A third ending would have taken additional writing effort, to no immediately obvious didactic purpose.
A necessary condition for a third ending might involve a solution that purposefully violates the criteria in some respect.