You see, it takes logic to solve a Sudoku puzzle. It is like a riddle. You look for clues in the given puzzle, such as I explain in my article on Sudoku Tips.
You use logic. Ask yourself, what numbers can I exclude from this cell? You may find a pair, two cells that contain the same two numbers. Let’s say 4 and a 6.
If more than two cells in a row, column, or 3×3 matrix contain the candidates 4 and 6, we can logically conclude that if two cells will have the values 4 and 6, then it is safe to remove the numbers 4 and 6 from all other cells in that row, column or 3×3 matrix.
That is an easy brain tickler. Sudoku offers many brain challenges. Try this one.
In the graphic above, there are four cells circled in red from a partially solved Sudoku puzzle. All four cells reside in two adjacent 3×3 matrix regions. Given the candidates as shown, can you solve one of the four cells with the information given?
As you will note, all four cells contain the numbers 2 and 8. One cell of the four also contains the number 1.
This brain teaser requires a little logic. If you remove the 1 from the cell that contains three numbers, you get the situation where all four cells would then contain the numbers 2 and 8.
The four cells then would make the puzzle unsolvable. There would be two possible solutions to the puzzle. Since a well-formed Sudoku puzzle only has one solution, we can conclude that removing the 1 is not possible.
When you see this pattern, enter the stand-alone number (1) in the cell that contains the three numbers. It will allow you to solve the rest of the puzzle.
You will find this brain teaser in more difficult puzzles. I have encountered it only about a half dozen times.
For this technique to work, the four cells must reside in only two 3×3 regions. If they are in four 3×3 regions, then they might not work.
For more information about this technique, I highly recommend that you buy the book
Mensa Guide to Solving Sudoku: Hundreds of Puzzles Plus Techniques to Help You Crack Them All (Mensa) by Peter Gordon. I give Peter credit for naming this technique the Gordonian Rectangle.