Every troll is either a knight or a knave. Knights tell only the truth and knaves tell only lies. As a census taker for the Land of Trolls, you approach a group of $5$ trolls and ask each how many knights are in the group; two of them say $0$, two of them say $2$, and one of them says $4.$ How many knights were there? As mathematicians, we want to know things like how many $n$-troll puzzles are there? How many of those puzzles have unique solutions? And how do these numbers relate as $n$ goes to infinity? Gabe will tell the story of how a probabilistic perspective unlocked the beautiful combinatorics of these puzzles, proving (partially by coincidence) that the limiting proportion of puzzles with no solution equals the limiting probability that a large binary matrix is nonsingular.