The number of different digits determines solution and verification of multiplication problems

The solution and verification of single-digit multiplication problems vary in speed and accuracy. The current study examines whether the number of different digits in a problem accounts for this variance. In Experiment 1, 41 participants solved all 2–9 multiplication problems. In Experiment 2, 43 participants verified these problems. In Experiment 3, 26 participants solved 10 problems that differed in shared-digit network (SDN) size and matched in problem size. In Experiment 4, 24 participants verified these matched sets. Results show faster and more accurate responses to problems that include fewer different digits relative to problems with more different digits, and faster and more accurate responses to problems whose SDN is small relative to problems whose SDN is large. We thus show that the number of different digits in a problem, including the operands and the solution, determines the speed and accuracy of its solution and verification. This parsimonious account also explains why responses to five and tie problems, which include fewer different digits relative to nonfive and nontie problems, are faster and more accurate than responses to other problems.