Sudoku Solutions: Helpful for Some, Boring for Others

Sudoku puzzle solved by a brute force/backtracking algorithm. The algorithm started by filling the first empty cells with the values 1 - 9 until one of them created a valid board and moved on from there backtracking whenever doing this could not create a valid board. The program is written in Java. Letter images made in Photoshop.
Photo: Wikimedia

Many players of the Sudoku find this puzzle game very difficult to solve. However, because of the clever minds of most players, they have created techniques, strategies, and solutions to make the game simple.

The following are some of those solutions the players have made in solving any levels of the Sudoku puzzle game.

1.  Scanning

This solution is executed at the start and all throughout the game. Scans should be done for many times in the middle of studying the puzzle. There are actually two basic techniques involved in scanning they are:

•  Cross-hatching – This is scanning of rows and columns to know which line holds numbers that should be removed. The process is repeated in rows and columns. For an accurate result, the numbers should be scanned based on their frequency. It is very necessary to do this process in order to check all the 1 to 9 numbers. 

•  Counting – This technique is performed to know what the missing numbers are. In order to have a fast result, counting should be done based on the last number revealed. 

While the scanning is performed, advanced solvers are searching for possibilities. They do it by narrowing the location of each number in a row or column. 

Most challenging puzzle games have many possibilities that need to be discovered. These possibilities might be in many directions or intersections. The puzzles that need only the solution for scanning in order to be solved are categorized as the easy puzzle. On the contrary, the difficult puzzle can also be solved by using scanning but still, it requires the discovery of possibilities. 

2.  Marking Up

Scanning is usually stopped when there are no numbers that can be detected. From this, it is important to use some logical analysis. Most players find it helpful to lead the analysis by marking up the possible numbers in the empty boxes. There are two famous notations in marking up, they are:

•  Subscript – The possible numbers are written in subscript in the box. The disadvantage to this is that Sudoku puzzle found in newspapers or magazines are normally too small to contain the subscripts. Therefore, it is suggested that if you are going to use this notation, you should make a bigger copy of the puzzle or use a finely pointed pencil. 

•  Dots – the advantage of this is that it can be used on original puzzles. When using the notation, you need to have dexterity in order to put the dots. Misplaced or unintended dots may lead the player to confusion. 

3.  Analyzing 

The following are the two basic approaches for analyzing:

•  Elimination – This is the way of eliminating possible numbers from one box or more to have only one option. After getting each answer, it would be good to perform another scan. This is made to know the effect of the last number placed in. There are several elimination tactics. The commonly used among these tactics is the unmatched candidate removal. Boxes with similar sets of possible numbers are a match if the number of the possible numbers is equal to the numbers of boxes having them. 

•  What if – In this approach, a box containing only two possible numbers is chosen and a guess is completed. The steps already mentioned are repeated except if the same number is found in the same box. If duplication happens, the alternative candidate number is the solution. In logical expressions, this is what called as the reductio ad absurdum. This kind of approach requires a pencil and an eraser. The logical perfectionist may frown about this approach because of its many trial and error test. However, this approach can draw out solutions faster. 

It is not necessary to combine techniques in order to solve the Sudoku. These may prevent the drawbacks of the above solutions, which for most players can be very uninteresting. The counting of the rows and columns can also bore the seasoned Sudoku players. Writing down the possible numbers in an empty box can also consume more time. In addition, the what-if approach can be very puzzling unless the players know how to organize. 

The best solution for solving the Sudoku is to search for techniques that do not require more counting, marking out and analyzing.

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