The Psychology of Su Doku Problems

Three experiments addressed the questions: what tactics do individuals use to solve Su Doku puzzles, and what determines the difficulty of using these tactics? A typical Su Doku consists of an array of 9x9 cells; the array is divided into nine boxes of 3x3 cells. Some of the cells in the array already contain digits. The task is to fill in all the empty cells so that each row, column, and box contains each of the digits 1 to 9 once and only once. The puzzles can be solved using pure deduction. Both simple and advanced tactics exist for Su Dokus, and Figure 1 illustrates them. Simple tactics call for one-step deductions of definite digits. X must be 5, because 5 is already in the columns and row that intersect all the empty cells in the box containing X. Advanced tactics call for multi-step deductions of both possible and definite digits, and the listing of possible digits for cells. The only possible digits for Y are 4, 6, 9, but the only possible digits for the two empty cells in the row above Y are 6, 9. Hence, Y cannot be either of these two digits, and so it must be 4.