Solving Techniques

Look for a row with only one empty cell left. Then find out what digit is missing in that row and fill the empty cell with it. That’s it. The same works for columns and 3 x 3 blocks. In the first example below you can place digit 9 in row 7. In the second example you can place digit 6 in block 8.

Select a 3 x 3 block and a digit. Check how many cells in that block can contain the selected digit. If there is only one such cell, you can fill that cell with the selected digit. The same logic is applicable for rows and columns. A cell can contain a digit if there is no such digit in the same row, column and 3 x 3 block.

Select a cell and check how many digits are allowed in that cell. If there is only one allowed digit, you can fill the cell with that digit. A digit is allowed in cell if there is no such digit in the same row, column and 3 x 3 block. In the first example below the highlighted cell can contain only digit 3. In the second example - only digit 4.

Select a 3 x 3 block and a digit. If all possible cells for that digit lie in one row, the digit cannot appear anywhere else in that row outside the block. The same works for a column. Learn why this works, see pointing pairs and triples in action, and use the eliminations to find your next single.

Select a row or column and a digit. If all possible cells for that digit lie in one 3 x 3 block, the digit cannot appear elsewhere in that block outside the selected line. Learn why this works, compare Claiming with Pointing Candidates, and use the eliminations to reveal Hidden Singles.

If two missing digits can each go in only the same two cells of a row, column or block, those cells must contain that pair. Remove every other candidate from the two cells. Learn to spot Hidden Pairs with and without pencil notes, and use the eliminations to reveal Hidden Singles.

Find three missing digits whose only possible positions in a row, column or block lie in three cells. Reserve those cells for the three digits and remove every other candidate from them. The digits need not appear in all three cells. Follow the pencil-note examples and interactive demo, then practice with prepared library puzzles.

Find two cells in a row, column or block that each contain only the same two candidates. Those digits must occupy the two cells, so remove them from every other cell in that group. Follow the pencil-note examples and interactive demo to see how eliminations help you make progress, and compare Naked Pairs with Hidden Pairs.

Find three cells in a row, column or block whose complete candidate lists contain only three digits between them. Those digits belong in the three cells, so remove them from the other cells in that group. The lists need not match. Follow the pencil-note examples and interactive demo to see how a triple can lead to a single or to further candidate eliminations.

Find four cells in a row, column or block whose complete candidate lists use only four digits between them. Reserve those digits for the four cells and remove them from other cells in that group. The lists need not match or contain all four digits. Follow the pencil-note examples and demo, compare complementary hidden subsets, and practice with prepared library puzzles.