In reality, the question of whether things are authored at all is a contentious one, discussion of which violated board rules.In real life, everything that happened before now is pre-authored, including what is a prime number and what isn't (once the concepts of numbers and prime are determined).
But we are talking about solving problems. Problems can be solved although no solution is pre-authored: mathematics is an example. (No one authors prime numbers; their existence and identity is the outcome of the stipulation of a system of axioms.)
To address @EzekielRaiden also: another example, but one that is less well known than mathematics and so not one I've mentioned upthread, is legal reasoning. Legal reasoning provides methods of generating answers to questions that had not occurred to anyone when the law was authored. The answers are not pre-authored.
The general pattern that unifies mathematics and law is the existence of canonical inference rules. There are RPGs that have these too: rules and principles that direct how scenes are to be framed, and how consequences established.
That is how play can yield an outcome, including the solution of a mystery, although no single person authored it.