Method to Solve a Hard Sudoku Puzzle - Forcing Chain

Dr. Yaling Zheng

Whether you are traveling, taking a break, or recovering in hospitals, solving a number puzzle game (Sudoku Puzzle)  would be a perfect brain workout for you! 

When you solve a hard Sudoku puzzle, forcing chain method can help you determine exactly what number a certain empty square must hold.

Forcing chains work in the following way: Start on the square R4C4 (the square in the fourth row and the second column), and fill in one of the two candidates, 3 or 4. The following I am going to show no matter R4C4 is 4 or 6, R1C3 will always be number 4. This is exactly a great example of forcing chain. 
​
If R4C4 is number 4, R1C4 has to be number 8 (step 1), and then R1C3 has to be number 4.

If R4C4 Iis number 3, R4C7 has to be number 4 (step 1), and then R5C9 has to be number 3 (step 2), and then R3C9 has to be number 4 (step 3), and then R3C3 has to be number 8, and then R1C3 has to be number 4.

Therefore, no matter what number R4C4 is, R1C3 will be number 4. This is a great example of using forcing chain to determine a certain number for an empty square.  Forcing chain is an advanced method for expert Sudoku solvers. It takes time and patience to find forcing chain patterns. And I only recommend you use this method if all other simpler methods do not work. 

Today's Sudoku (Difficulty Level: Hard)