Ok.. that worked cool.

The concept I went on is just like the spreadsheet I posted. There are 8 different logic deductions at use. The first Solve_GridSingles() is the only one able to actually solve any cells... all the rest just remove possibilities.

Solve_GridSingles() is the only method able to solve a cell. All the rest just drop possibilities from cells. When there is only one possibility.. this method will solve it and in solving that cell will remove that possibility from all other cells in its Row, Column, and Cell Block. Its wrapped in a while loop because there is a fair likelihood that the removal of possibilities just caused another cell to have only one possibility. It continually keeps running until there are no cells for which there are only one possibility.

Solve_RowSingles() looks at cells in each Row to determine if there is only one possible location in that row for a number. If it finds one.. the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

Solve_ColumnSingles() looks at cells in each Column to determine if there is only one possible location in that column for a number. If it finds one.. the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

Solve_CellBlockSingles() looks at each Cell Block to determine if an unsolved number is possible in only one cell in a Cell Block. If true... the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

These are the 4 'basics'. I've broken out the more advanced once with an if. Basically if anything in the 4 basics changes anything.. the 4 basics need to get run again.

The 4 advanced deductions are a bit harder to explain.

Remove_Row_CellBlock_Isolation_Possibilities

Look at a row. If an unsolved number is possible in only one cell block, that number can not appear in any other row of the cell block.

Remove_Col_CellBlock_Isolation_Possibilities

Look at a Column. If an unsolved number is possible in only one cell block, that number can not appear in any other Column of the cell block.

Remove_CellBlock_Row_Isolation_Possibilities

Look at a CellBlock. If an unsolved number is possible in only one row of a cell block, that number can not appear in any other cell in that row in any other Cell Block.

Remove_CellBlock_Col_Isolation_Possibilities

Look at a CellBlock. If an unsolved number is possible in only one column of a cell block, that number can not appear in any other cell in that column in any other Cell Block.

Once again.. keep looping until all 8 have failed. At this point the rubber has met the road. Selective Solutioning is in order.

Selective Solutioning which I provided the method for does the following. It will loop through every unsolved cell. It will grab the first unsolved cell.. loop based on the number of possible numbers that cell can have... pull out the first possibility, and then the magic happens. It will create a completely new grid based on the old grid, force that cell to have the value of the first possibility, and then call the Solve() for the grid. Solve() returns 2 possible values.. it either Solves or Breaks. A Break is what happens when there are no possibilities for a cell. At this point you picked the wrong value and if it breaks... on return remove that value as a possibility from our grid, delete the grid, and then try the next possibility. If all possibilities fail.. its just as broken so thats the set of retval after the loop.

Now.. once it goes into the solve it'll repass the 8 methods to deduce as much as possible. But you could just as likely deadlock and end up in Selective Solutioning again. No worries.. SS will do exactly what it did above.

The concept I went on is just like the spreadsheet I posted. There are 8 different logic deductions at use. The first Solve_GridSingles() is the only one able to actually solve any cells... all the rest just remove possibilities.

Solve_GridSingles() is the only method able to solve a cell. All the rest just drop possibilities from cells. When there is only one possibility.. this method will solve it and in solving that cell will remove that possibility from all other cells in its Row, Column, and Cell Block. Its wrapped in a while loop because there is a fair likelihood that the removal of possibilities just caused another cell to have only one possibility. It continually keeps running until there are no cells for which there are only one possibility.

Solve_RowSingles() looks at cells in each Row to determine if there is only one possible location in that row for a number. If it finds one.. the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

Solve_ColumnSingles() looks at cells in each Column to determine if there is only one possible location in that column for a number. If it finds one.. the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

Solve_CellBlockSingles() looks at each Cell Block to determine if an unsolved number is possible in only one cell in a Cell Block. If true... the Possibilities for that cell are set to that value only. The GridSingles will solve it on the next pass.

These are the 4 'basics'. I've broken out the more advanced once with an if. Basically if anything in the 4 basics changes anything.. the 4 basics need to get run again.

The 4 advanced deductions are a bit harder to explain.

Remove_Row_CellBlock_Isolation_Possibilities

Look at a row. If an unsolved number is possible in only one cell block, that number can not appear in any other row of the cell block.

Remove_Col_CellBlock_Isolation_Possibilities

Look at a Column. If an unsolved number is possible in only one cell block, that number can not appear in any other Column of the cell block.

Remove_CellBlock_Row_Isolation_Possibilities

Look at a CellBlock. If an unsolved number is possible in only one row of a cell block, that number can not appear in any other cell in that row in any other Cell Block.

Remove_CellBlock_Col_Isolation_Possibilities

Look at a CellBlock. If an unsolved number is possible in only one column of a cell block, that number can not appear in any other cell in that column in any other Cell Block.

Once again.. keep looping until all 8 have failed. At this point the rubber has met the road. Selective Solutioning is in order.

Selective Solutioning which I provided the method for does the following. It will loop through every unsolved cell. It will grab the first unsolved cell.. loop based on the number of possible numbers that cell can have... pull out the first possibility, and then the magic happens. It will create a completely new grid based on the old grid, force that cell to have the value of the first possibility, and then call the Solve() for the grid. Solve() returns 2 possible values.. it either Solves or Breaks. A Break is what happens when there are no possibilities for a cell. At this point you picked the wrong value and if it breaks... on return remove that value as a possibility from our grid, delete the grid, and then try the next possibility. If all possibilities fail.. its just as broken so thats the set of retval after the loop.

Now.. once it goes into the solve it'll repass the 8 methods to deduce as much as possible. But you could just as likely deadlock and end up in Selective Solutioning again. No worries.. SS will do exactly what it did above.