You might have solved sudoko if not try solving it LINK.
Only 3 main constrains
A number among 1-9 appears
1. Only Once is a row
2. Only Once in a column
3. Only Once in a 3 x 3 matrix
Programatically it can be solved in following manner. Each successive step is improvement above it
Possibilities - 9 values per square, Total = 10^38 possibilities
Time : it takes billion of years to solve it. 13.5 Billion Year Solar system started forming.
Use Back tracking
Greatly reduces the number patterns generated to match input.
Choose 1st available empty cell, Choose 1st available safe value
Continue filling for rest of empty cells.
Constrain on empty Cells
Greatly reduces the number of paths taken during back tracking.
Search for empty cell which has least possible values, ie. the probability of failure reduces
Constrain on values possible per empty Cell
Further reduce the probability of failure.
Pick up value in the cell which least probability to fail by 1 step further.
