How do people ask questions to zero in on a correct answer? Although we can formally define an optimal query to maximize information gain, algorithms for finding this optimal guess may impose large resource costs in space (memory) and time (computation). To understand how people trade off the information gain and the computational difficulty of choosing the ideal query, we turned to a large dataset of 380,000 guesses made during a number-guessing game with Amazon Alexa. We analyzed whether the arithmetic difficulty of following the optimal strategy predicts how far a guess deviates from theoretically optimal query. We find that when memory load is higher, and when more arithmetic operations need to be performed, human guesses deviate more from the most informative query. These results suggest human computational resource constraints limit how people seek out informative questions.