Lesson 13 of 14 · Cross-line technique

Swordfish: three lines working together

The guide and all sudoku lessons
The full guide Playing on Puzzled
  1. 1The last empty squareFirst move
  2. 2ScanningCore technique
  3. 3Naked singlesCore technique
  4. 4Pencil marksSolving aid
  5. 5Hidden singlesCore technique
  6. 6Naked pairsPair technique
  7. 7Pointing pairsPair technique
  8. 8Hidden pairsPair technique
  9. 9Naked triplesSubset technique
  10. 10Hidden triplesSubset technique
  11. 11X-WingCross-line technique
  12. 12XY-WingWing technique
  13. 13SwordfishCross-line technique
  14. 14JellyfishCross-line technique

Swordfish takes the X-Wing idea from two starting lines to three. Choose one digit and three rows where it has only two or three possible homes in each row. If all those homes lie in the same three columns, you have a row-based Swordfish.

Each starting row needs that digit once. The three placements must use different columns, so they use all three of the crossing columns. Remove the digit from those columns outside the three starting rows. You do not need to work out which of the possible arrangements is the right one.

You can turn the rule around: three starting columns can confine the digit to three rows. The pattern does not need a candidate at all nine intersections. Two homes in each starting line can be enough, as the examples show.

The diagrams show every pencil mark in the shaded lines, calculated from the displayed board. The digit we are tracking is emphasised, the six supporting squares have a darker blue tint, and the green outline marks one target. Other candidates in those squares are allowed.

Example 1: Start from three columns

Step 1 of 5

Track 5 in columns 3, 4 and 9. Read each whole column: its only possible homes are among the six darker blue squares.

Look for 5 in columns 3, 4 and 9. Column 3 allows it only in rows 2 and 5; column 4 only in rows 2 and 4; column 9 only in rows 4 and 5. Between them, these columns use just three rows: 2, 4 and 5.

Each of those columns must supply one 5, and no two of those 5s can share a row. That accounts for the 5 in all three rows. The target at row 2, column 1 is outside the starting columns, so remove its 5. Keep 2, 3 and 4.

Example 2: Turn the pattern around

Step 1 of 5

Track 1 across the full length of rows 3, 4 and 9. Each row has two possible homes for it, shown in darker blue.

Now track 1 in rows 3, 4 and 9. Row 3 has homes in columns 6 and 7; row 4 in columns 6 and 9; row 9 in columns 7 and 9. All six homes fit in columns 6, 7 and 9.

Those rows must put their three 1s in different columns, using all three of columns 6, 7 and 9. Row 1, column 6 lies in a crossing column but outside the starting rows. Remove its 1, leaving 2, 5 and 6. The same argument can remove other 1s in those columns outside rows 3, 4 and 9; we show one target at a time.

Example 3: An extra home breaks the pattern

Step 1 of 5

Look at the six darker blue 4s in rows 3, 5 and 6, at columns 4, 6 and 7. Do not accept the pattern yet.

The six darker blue 4s in rows 3, 5 and 6 fit in columns 4, 6 and 7. That looks promising, but there is another 4 at row 5, column 1. Count all the homes in the starting rows, not just the ones that make a neat pattern.

The three rows actually use four columns: 1, 4, 6 and 7. If row 5 takes its 4 in column 1, the three rows need not use all the other columns. This is not a basic Swordfish. Keep the 4 at the proposed target, row 4, column 6.

Try it yourself

A new board, and the same idea. Get it wrong and the board tells you why.

Track 8 in rows 1, 6 and 9. Their darker blue homes lie in columns 2, 8 and 9. Which candidate can this Swordfish remove from the green-ringed target at row 3, column 2?

Pick one candidate to cross out in the ringed square, not a digit to place.

How to spot it faster

  • Pick one digit. Look for starting rows with two or three homes, then compare their column numbers. Three such rows must fit in exactly three columns. Try the same search from columns if the rows do not help.
  • Check every square along each starting line. An extra home outside the three crossing lines invalidates a basic Swordfish. Extra homes on the crossing lines outside the starting lines are the candidates you can remove.
  • Use accurate notes and try simpler moves first. The useful part is the confinement, not a shape drawn between the squares; the six homes in these examples are enough.

Common mistakes

Looking for nine matching intersections

A Swordfish need not fill a three-by-three lattice of candidates. A starting line can use just two of the three crossing lines. What matters is that every possible home on all three starting lines fits inside the same three crossing lines.

Removing from the starting lines

When you start from rows, the removals are in the crossing columns outside those rows. Starting from columns reverses the rule. Do not remove any of the supporting candidates: the pattern does not tell you which of them will be filled.

Questions

Further reading

Try it

Try an expert 9×9 and compare one digit's possible homes after simpler moves run out. A random expert deal may need a different technique, so use the boards and exercise here for targeted Swordfish practice. Free hints still stop at pairs.

Play solo on an expert 9×9