In this study, we consider a 9x9 post-filled Sudoku puzzle as an example of a three factorial design without blocking. Because of the rigidity of Sudoku, the all main effects and two factors interactions are all statistically insignificant. The three factor interaction is can be statistically significant or not. The use of column or row additions in the computation of the 3-factor interactions of a chosen Sudoku yields complementary results. If the rows addition gives an interaction effect that is statistically significant then the column result will be insignificant and vice versa. The treatment effects of the 3-factor effect of a post-filled Sudoku depend on whether the column or row sums are used in the computation of the interaction effect.
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