Swordfish

The pattern

Take a digit and three rows. In each of those rows, the digit must be restricted to cells that fall within the same set of three columns. It does not have to be possible in all three columns in every row — two are enough, as long as nothing spills outside the set.

Then those three columns take the digit in those three rows, and it can be erased from the rest of each of the three columns.

The condition people get wrong

A Swordfish does not require exactly two candidates per row. That stricter version is easier to see but misses most real Swordfish patterns. The actual requirement is containment: every possible position for the digit in each of the three rows lies inside the chosen three columns.

As with the X-Wing, the whole thing works with rows and columns swapped.

How to search without going mad

Pick a digit that is already placed six or seven times. List, for each unsolved row, the columns where it can still go. Rows with two or three columns are candidates. Then look for three such rows whose column sets union to exactly three columns.

If the union grows to four, stop and move on. Swordfish hunting rewards discipline in abandoning near-misses quickly.

Why it is valid

Three rows must each place the digit, and all their options are inside three columns. Three digits into three columns fills them, so no other cell in those columns can hold the digit. It is the X-Wing argument with three lines instead of two.