We present an information-theoretic approach to modeling childrens performance in a deductive reasoning game. Ourapproach takes cognitive limitations into account to model the interpretability of feedback that children receive during thegame. We use data of thousands of children, 5 to 12 years of age, from a popular online educational learning system. In theDeductive Mastermind game the player seeks to identify a hidden code that consists of a sequence of colors. The playersees a series of proposed codes together with corresponding feedback providing partial information about the similarity ofeach proposal and the hidden code. In Deductive Mastermind games, the proposals are set up such that deductive reasoningleads to a single possible hidden code. The games vary in code length, the number of possible colors, and the number ofproposals, resulting in game difficulties of various degrees.

Deductive Mastermind is a deductive reasoning game that isimplemented in the online educational game system Math Gar-den. A good understanding of the difficulty of Deductive Mas-termind game instances is essential for optimizing the learningexperience of players. The available empirical difficulty rat-ings, based on speed and accuracy, provide robust estimationsbut do not explain why certain game instances are easy or hard.In previous work a logic-based model was proposed that suc-cessfully predicted these difficulty ratings. We add to this workby providing a model based on a different logical principle—that of eliminating hypotheses (dynamic epistemic logic) in-stead of reasoning by cases (analytical tableaux system)—thatcan predict the empirical difficulty ratings equally well. Weshow that the informational content of the different feedbacksgiven in game instances is a core predictor for cognitive dif-ficulty ratings and that this is irrespective of the specific logicused to formalize the game.