The psychological puzzle of Sudoku

Abstract

Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 × 9 array according to the general rule that every digit from 1 to 9 must occur once in each row, in each column, and in each of the 3-by-3 boxes in the array. We present a theory of how individuals solve these puzzles. It postulates that they rely solely on pure deductions, and that they spontaneously acquire various deductive tactics, which differ in their difficulty depending on their “relational complexity”, i.e., the number of constraints on which they depend. A major strategic shift is necessary to acquire tactics for more difficult puzzles: solvers have to keep track of possible digits in a cell. We report three experiments corroborating this theory. We also discuss their implications for theories of reasoning that downplay the role of deduction in everyday reasoning.