Progress without filling a square

Learn why a proved elimination is a useful move.

Placement and elimination differ

A placement proves the one digit that belongs in a cell. An elimination proves one digit that cannot belong there. Eliminating 7 from {2, 4, 7} leaves {2, 4}; you have made progress even though you cannot yet fill the square.

For example“This cell is not 7” does not mean “this cell is 2.” There may still be more than one possibility.

A box can reserve part of a row

Suppose every possible 6 in a box lies in the same row. The box must put its 6 in one of those cells. Wherever it goes, that row already receives its 6 inside the box. Remove 6 from the rest of the row outside the box. This is pointing.

For exampleIf box 1 allows 6 only at r2c1 and r2c3, remove 6 from r2c4 through r2c9 wherever it is still a candidate.

Run both cases

Do not choose between the two candidate cells. If the first is 6, the outside target cannot be 6. If the second is 6, the same target still cannot be 6. Because these are all the possibilities, the target is excluded either way.

For exampleYou may know that a digit lives in a small group without knowing which cell holds it.

Look for the counterexample

Before applying a pattern, try to break the argument. Is there another 6 elsewhere in the box, outside that row? If so, the box could use that other location and the row would no longer be reserved. That extra candidate makes the proposed pointing argument fail.

For exampleA third 6 at r3c2 breaks the pattern. A third 6 at r2c2 keeps every possibility on row 2 and makes a pointing triple.

Quick check

All three possible 8s in a box lie in one column. What does this prove?

Place 8 in the first of those cells.
Remove candidate 8 from the column outside that box.
Remove every other digit from the three cells.

Show the answer

Remove candidate 8 from the column outside that box. Correct. Whichever box cell becomes 8, the rest of the column cannot contain another 8.

Try it with the interactive lessons Play an easy puzzle

Next, when you are ready: Pointing pair.