How to : How to Solve Sudoku when Stuck

If only one number fits in a cell, then it has to go there. After you fill in your notation, you might find some obvious cells to fill in that you missed earlier. Scan through each of the cells on the puzzle and see if there are any with just one possible solution. Since you know that no other numbers can fit there, that number is the only solution for that cell.^[2]

Cells with 2 numbers in the same row, column, or box limit other cells. Check for 2 cells in the same row, column, or box that can only contain the same 2 possible numbers, which is known as a “naked pair.” Even though you don’t know exactly which number goes into each square, you can erase your notation for the other cells in the row, column, or box since they can never contain those values.^[3]

Triples have only 3 possible numbers that could fit into the 3 cells. All 3 cells have to be in the same row, column, or box. “Naked” triples only have the 3 potential numbers while “hidden” triples have extra digits in the cells that make them harder to spot. All 3 of the potential candidates don’t have to appear in each of the cells, which can make them a little trickier to find.^[4]

Eliminate numbers from a row or column if they’re constrained to one box. Pointing pairs and triples are when there are only 2 or 3 cells with the same potential numbers in a 3 x 3 box. The cells must also be in the same row or column. Since you know that the number has to go in one of those 2 cells, you can erase any other time you notated the number in the same row or column.^[5]

Test a number in a cell with 2 digits to see how it affects the other cells. To use a forcing chain, look for multiple cells that have 2 potential numbers. You should be able to draw lines through the rows and columns to connect all the cells in the chain. Test each number in one of the cells and check how they fill in the rest of the chain. If there’s one cell that uses the same number no matter which digit you filled in originally, then you can assume that it’s the only solution.^[6]

The X-wing technique reveals numbers for cells in 2 columns and rows. To use an X-wing, check for a row that has a potential candidate that can only fit into 2 cells. Check for another row in the puzzle that has the same candidate in 2 cells that are in the same columns as the first row candidates. The potential number can only fit once in each of the columns, so you can erase it from any other cells in those columns.^[7]

You can eliminate numbers from intersections between rows and columns. Start by finding a cell with only 2 possible numbers to use as a “pivot.” Check the same row, column, and box for “pincers”, which are other cells with 2 potential candidates that share at least 1 number with the pivot. The second number in each of the pincers should be the same. Check the cell where the pincers would intersect on the puzzle to see if it shares a number with them. If it does, then you can eliminate it from the puzzle.^[8]

Rule out numbers when 3 cells with 2 values each form an angle. The values should only have 3 different potential numbers between them. If one cell has candidates X and Y and the other 2 cells could be X and Z or Y and Z, then no other cells in the same row, column, or box can contain the Z value.^[9]

Test the possibilities in a chain of numbers found in 3 rows or columns. Check your puzzle for 3 separate rows or columns where a potential digit can only fit into 2 or 3 cells in each. You should be able to connect the cells if you drew lines through the columns and rows. After you connect all of the cells you can erase the potential candidate from any other cells in those rows or columns.^[10]