Claiming Candidates

Hard

Description

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

Why? The row or column must contain the digit somewhere, and all its possible positions are in this block. One of those cells will supply the block's copy of the digit. No other cell in the block can contain it, even though you do not yet know which of the possible cells will.

Each example shows two steps: use Claiming Candidates to rule out a position, then place the Hidden Single it reveals. The purple cells remain possible throughout the deduction.

Example 1. A row claims a block

1. Claiming Candidates
The 8 at row 4, column 4 rules out row 8, column 4. Row 8 can contain 8 only at columns 7 and 9, both in block 9. This rules out 8 from row 9, column 8. The 8 at row 4, column 4 rules out row 8, column 4. Row 8 can contain 8 only at columns 7 and 9, both in block 9. This rules out 8 from row 9, column 8.
The highlighted 8 in column 4 rules out row 8, column 4. Only the two purple cells remain for 8 in row 8, both inside block 9. So 8 cannot go elsewhere in that block, ruling out row 9, column 8.
2. Hidden Single
Hidden Single 8 in column 8, at row 3. The existing 8 in row 4 rules out row 4, column 8, and Claiming rules out row 9, column 8. Hidden Single 8 in column 8, at row 3. The existing 8 in row 4 rules out row 4, column 8, and Claiming rules out row 9, column 8.
Column 8 has three empty cells. The existing 8 in row 4 rules out one, and Claiming rules out row 9, column 8. Only the green cell remains: row 3, column 8 must be 8.

Example 2. A column claims a block

1. Claiming Candidates
The existing 5s in rows 8 and 9 rule out the bottom two empty cells of column 5. Only rows 2 and 3 remain possible for 5 in that column, both in block 2. This rules out 5 from row 1, column 6. The existing 5s in rows 8 and 9 rule out the bottom two empty cells of column 5. Only rows 2 and 3 remain possible for 5 in that column, both in block 2. This rules out 5 from row 1, column 6.
The highlighted 5s in rows 8 and 9 rule out the bottom two empty cells of column 5. Its only possible 5s are the two purple cells in block 2. That block must get its 5 in column 5, ruling out row 1, column 6.
2. Hidden Single
Hidden Single 5 in row 1, at column 7. The existing 5 in column 3 rules out row 1, column 3, and Claiming rules out row 1, column 6. Hidden Single 5 in row 1, at column 7. The existing 5 in column 3 rules out row 1, column 3, and Claiming rules out row 1, column 6.
Row 1 has three empty cells. The existing 5 in column 3 rules out one, and Claiming rules out column 6. The green cell at row 1, column 7 is now the only possible position for 5 in the row.

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 Claiming Candidates

  1. Select a digit and a row or column where it is still missing.
  2. Find every possible position for that digit in the whole line. Existing copies of the digit in intersecting rows, columns and blocks help you rule cells out. With pencil notes, highlight the digit and check all its candidates along the line.
  3. If all those positions are inside one block, keep them and remove the digit from other cells in that block, outside the selected line. The line has claimed the block's copy of the digit.
  4. Recheck for Hidden Singles and Naked Singles. A candidate removal may leave only one position for a digit, or only one digit in a cell.

If there is nothing to eliminate in the rest of the block, try another line or digit. After a placement, check again: the new digit may create another claiming opportunity. Keep pencil notes up to date, and make sure they contain every remaining possibility. A missing note can make an invalid pattern look convincing.

Two or three possible positions

Claiming works with two or three candidates for one digit, as long as all the digit's candidates in the selected line belong to one block. The cells can have other candidates too. You are eliminating possibilities elsewhere, without choosing which of these cells holds the digit.

If the row or column has only one possible position for the digit, it is already a Hidden Single. Place it immediately. The examples here need Claiming because more than one position remains in the source line.

Check the whole row or column

Two candidates together in one block are not enough. If the digit is also possible farther along the same row or column, that line does not force it into this block. The demo's final check shows how one overlooked candidate defeats the elimination.

Keep the candidates in the intersection. Remove only the same digit from cells inside the block but outside the selected line. Other digits in those cells are unaffected.

Claiming or Pointing?

For Claiming, start with a row or column: all its possible positions for a digit lie in one block, so eliminate elsewhere in that block. For Pointing Candidates, start with a block: all its possible positions for a digit lie in one row or column, so eliminate farther along that line, outside the block.

Both techniques use the rule that each group contains a digit exactly once. What matters is which group confines the digit, and which other group loses candidates.

Try it yourself

Each puzzle opens where Claiming Candidates reveals a Hidden Single. Find the claiming pattern, rule out the affected candidates, then look for the digit's only remaining position in a row or column. Use Hint to follow the reasoning step by step.

  • Sudoku #1 — find a row that claims a block.
  • Sudoku #2 — find a column that claims a block.
  • Sudoku #3 — find a claiming pattern that removes candidates from several cells.

See also