Pointing Candidates

Hard

Description

Select a 3x3 block and a digit that is still missing from it. If all possible cells for that digit lie in one row, you can rule it out in the rest of that row, outside the block. The same works for a column.

The block must contain the digit somewhere. Since every possible position lies in the same row or column, that line will get the digit inside the block. It cannot contain another copy outside the block. You can make this elimination even before you know which cell inside the block will hold the digit.

Each example shows two steps: use Pointing Candidates to rule out positions, then place the Hidden Single it reveals.

Example 1. Pointing pair in a row

The 9 at row 9, column 7 rules out 9 from row 4, column 7. In block 6, only row 5, columns 8 and 9 remain possible for 9. This pointing pair rules out 9 from row 5, column 3. — The highlighted 9 at row 9, column 7 rules out 9 from row 4, column 7. That leaves only the two purple cells in row 5 for 9 in block 6. So 9 cannot go elsewhere in row 5, ruling out row 5, column 3.

Hidden Single 9 in block 4, at row 6, column 3. Pointing rules out row 5, column 3; the existing 9s at row 7, column 1 and row 2, column 2 rule out row 6, columns 1 and 2. — The existing 9s in columns 1 and 2 rule out two more cells in block 4. With row 5, column 3 ruled out by pointing, only the green cell remains: row 6, column 3 must be 9.

Example 2. Pointing triple in a column

The only possible 6s in block 5 are in column 4, rows 4, 5 and 6. This pointing triple rules out 6 from column 4, rows 1 and 2. — In block 5, all three possible positions for 6 are in column 4. This rules out 6 from the first two cells in that column, inside block 2.

Hidden Single 6 in block 2, at row 3, column 6. Pointing has ruled out the block's other two empty cells, at row 1, column 4 and row 2, column 4. — Those two eliminations leave just one possible position for 6 in block 2: the green cell at row 3, column 6.

Demo

Click on arrow buttons or use arrow keys on your keyboard to navigate between slides. Tap on arrow buttons to navigate between slides.

How to find Pointing Candidates

Select a digit and look at a block where it is still missing.
Find every cell in that block where the digit is possible. Existing copies of the digit in intersecting rows and columns help you rule cells out. With pencil notes, look for all remaining candidates for that digit in the block.
If all those cells share one row or column, follow that line outside the block and remove the digit from any other candidates along it. Keep the possibilities inside the block.
Recheck for Hidden Singles and Naked Singles. An elimination may leave one possible cell for a digit, or one possible digit in a cell.

If there is nothing to eliminate outside the block, continue your search in another block or with another digit. After a placement, check again: the new digit can create another pointing pattern. When using pencil notes, highlighting one digit at a time makes its positions easier to compare.

Pointing pairs and triples

Two possible cells in the line form a pointing pair; three form a pointing triple. Both use exactly the same logic. These names count the possible positions of one digit. The cells can still have other candidates, and you do not have to decide which cell holds the digit yet.

If the block has only one possible cell for the digit, you have a Hidden Single and can place it immediately. Pointing Candidates is useful when several positions remain, but their alignment already lets you make progress elsewhere.

Check the whole block

Finding two candidates in one row is not enough if the digit is also possible elsewhere in the block. Every possible position must lie in that same row. Check the same condition for columns. The demo's final example shows why overlooking another candidate would make the elimination invalid.

Remember the direction: start with the possible positions inside a block, then eliminate along the row or column outside that block. The related Claiming Candidates technique starts with a row or column and makes eliminations inside a block.

Try it yourself

Each puzzle opens at a position where Pointing Candidates reveals a Hidden Single. Find the pointing pattern, eliminate its candidates, then look for the only remaining position for that digit in a row, column or block. Use Hint to see the reasoning step by step.

Sudoku #1 — find a pointing pair along a row.
Sudoku #2 — find a pointing pair along a column.
Sudoku #3 — find a pointing triple.