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Algorithms often appear as 'black boxes' to non-expert users. While prior work focuses on explainable representations and expert-oriented exploration, we propose XAlgo-a generalizable interactive approach using question answering to explain deterministic algorithms to non-expert users who need to understand the algorithms' internal states (e.g., students learning algorithms, operators monitoring robots, admins troubleshooting network routing). We contribute a formal model that first classifies the type of question based on a taxonomy, and generates an answer based on a set of rules that extract information from representations of an algorithm's internal states, e.g., the pseudocode. A user study in an algorithm learning scenario with 18 participants (9 for a Wizard-of-Oz XAlgo and 9 as a control group) reports what kinds of questions people ask, how well XAlgo responds, and what remain as challenges to bridge users' gulf of understanding algorithms.