Whether you are traveling or recovering in a hospital, Sudoku is a perfect mental workout for you! It helps develop your logic thinking, patience, concentration to solve problems, and confidence. In my earlier article “How to Design a Sudoku within minutes,” I talked about the idea of designing a Sudoku in the exact REVERSE WAY of solving a Sudoku. If you want to create a Sudoku, you must be able to solve a Sudoku! In this article, following earlier methods – OneChoice and Elimination, I am going to show you two advanced solving methods – Interaction and Subset that used in solving medium Sudoku puzzles.

Interaction

RowBox-Interaction/ColumnBox-Interaction: If a number in a row/column has to be in one box, this number cannot appear in other empty squares of that box.

BoxRow-Interaction/BoxColulmn-Interaction: If a number in a box has to be in one row/column, this number cannot appear in other empty squares of that row/column.

Interaction Example: In the second column, number 1 only appears in the fourth box so other empty squares in the fourth box cannot be number 1

In the second column, number 1 only appears in the fourth box, therefore, either R5C2 or R6C2 will be number 1. If we look at the fourth box, because either R5C2 or R6C2 will be number 1, therefore, all other empty squares in the fourth box will not be number 1. That is, in the fourth box, neither R4C1 nor R5C3 will be number 1. Note: R5C2 is the square at the fifth row and the second column. The fourth box is the intersection of the fourth row to the sixth row and the first column to the third column.

Subset

If the union of candidate values of two/three/four empty squares in a row/column/box are a set of two/three/four different numbers, other empty squares in this row/column/box cannot be any of these two/three/four numbers.

Subset Example: In the third row, the union of candidate values of R3C6 and R3C8 is 3 and 5. Other empty squares in the third row (R3C1, R3C5, R3C7) cannot be 3 or 5.

In the third row, R3C6 and R3C8, their candidate values, combined together, are 3 and 5. Therefore, all other empty squares, including R3C1, R3C5, R3C7 in the third row, cannot be number 3 or 5.

Yaling Zheng, Ph.D., founder of https://www.createclassicsudoku.com, received a doctorate degree from the University of Nebraska-Lincoln, where her studies focused on constraint programming and machine learning. She lives in Greater Cleveland/Akron.