THINKING & REASONING, 2008, 14 (4), 342 – 364 The psychological puzzle of Sudoku N. Y. Louis Lee The Chinese University of Hong Kong, Shatin, Hong Kong SAR of China Geoffrey P. Goodwin University of Pennsylvania, Philadelphia, PA, USA P. N. Johnson-Laird Princeton University, NJ, USA Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 6 9arrayaccordingtothegeneralrulethateverydigit 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. Keywords: Deduction; Problem solving; Reasoning; Inferential strategies. Downloaded By: [University of Pennsylvania] At: 15:18 18 February 2009 Correspondence should be addressed to N. Y. Louis Lee, Department of Educational Psychology, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR of China. E-mail:
[email protected] We thank the editor for useful advice about the framing of the paper; Vittorio Girotto and two anonymous reviewers for helpful criticisms; Sam Glucksberg, Adele Goldberg, and Fabien Savary for helpful suggestions; and Winton Au and Fanny Cheung for their assistance in Hong Kong.