The Algorithms of Solving Sudoku

Sudoku puzzles are often ranked by difficulty. Perhaps surprisingly, the number of givens has little or no bearing on a puzzle's difficulty. A puzzle with a minimum number of givens may be very easy to solve, and a sudoku with more than the average number of givens can still be extremely difficult to solve.

Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required.

Some initial layouts of sudoku may have more than one solution and even no solution, but such are not considered proper Sudoku puzzles; like in most other pure-logic puzzles, a unique solution is expected.

The algorithm of solving any sudoku puzzle consists of 3 processes:

1. Scanning of rows/columns and regions looking for missed numbers to fill in by a process of elimination. Scanning comes to a halt when no further numbers can be discovered. At this point you should turn on your logical thinking.
2. Marking up suspected candidate numbers in the blank cells. There are two popular methods: subscripts and dots. In the subscript notation the candidate numbers are written in subscript in the cells. The second notation is a pattern of dots with a dot in the top left hand corner representing a 1 and a dot in the bottom right hand corner representing a 9.

   An alternative technique that some find easier is to mark up those numbers that a cell cannot have.

3. Analyzing.
   Here you eliminate candidates and make predictions "what-if". In elimination, progress is made by successively eliminating candidate numbers from one or more cells to leave just one choice. After each answer has been achieved, another scan may be performed.

   In the what-if approach, a cell with only two candidate numbers is selected, and a guess is made.

   In fact, all the above-mentioned techniques are overlapping in the process of solving sudoku. However, each player may find the only right technique for himself/herself.

   This is an example of Sudoku analysis: all the cells where we cannot use 8(as it the first digit we come across) are marked with red, all the cells where "8" is possible are with green crosses:

   

   Now we try to fill in the most complete row or column and mark up the next most complete row/column or region:

   

   Send us your algorithm of solving Sudoku puzzle! (contact at absolutist dot com, subject: Sudoku solution) Screenshots are more than welcome.