Lesson 14 of 14 · Cross-line technique

Jellyfish: four starting lines, four crossing lines

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

Jellyfish uses the same counting argument as X-Wing and Swordfish, with four starting lines instead of two or three. Pick one digit and four rows where it has two, three or four possible homes in each row. Every home in those rows must fit inside the same four columns.

Each of the four rows needs that digit once, and those four placements must be in different columns. That uses all four crossing columns. The digit can be removed from those columns outside the four starting rows, even though you do not yet know which supporting squares will be filled.

A column-based Jellyfish reverses the rule: four columns restrict the digit to four rows. You do not need a candidate at all sixteen intersections. The first example has only eight supporting candidates, two in each starting row.

The shaded lines show every pencil mark from the displayed board. Darker blue squares support the pattern; the green outline marks one removal target. The second example reflects the first board across its diagonal, so you can compare the row and column versions of the same argument.

Example 1: Four rows reserve four columns

Step 1 of 5

Track 9 along the full length of rows 3, 6, 8 and 9. Each row has two possible homes, shown in darker blue.

Track 9 in rows 3, 6, 8 and 9. Row 3 uses columns 3 and 6; row 6 uses columns 2 and 7; row 8 uses columns 2 and 3; row 9 uses columns 6 and 7. The combined list is columns 2, 3, 6 and 7.

Those four rows must put their 9s in four different columns. They therefore account for the 9 in each of columns 2, 3, 6 and 7. Row 2, column 2 lies in a crossing column but outside the starting rows: remove its 9, keeping 2, 5 and 8. The same argument can remove other 9s on those columns outside the four starting rows; we show one target at a time.

Example 2: The same board, reflected

Step 1 of 5

On the reflected board, track 9 down the whole of columns 3, 6, 8 and 9. Each has two possible homes.

This is the first board reflected across its diagonal, not a new deal. The starting rows have become columns 3, 6, 8 and 9. Look for 9 in each: column 3 uses rows 3 and 6; column 6 uses rows 2 and 7; column 8 uses rows 2 and 3; column 9 uses rows 6 and 7.

Those four columns supply a 9 in each of rows 2, 3, 6 and 7. The target at row 2, column 2 is in a crossing row but outside the starting columns. Remove its 9 and keep 2, 5 and 8. The coordinates of this target happen to stay the same under the reflection.

Example 3: A fifth crossing line is one too many

Step 1 of 5

The darker blue 3s in rows 2, 5, 6 and 7 seem to fit inside columns 2, 3, 4 and 6. Check the whole of each starting row before accepting that picture.

The darker blue 3s in rows 2, 5, 6 and 7 fit in columns 2, 3, 4 and 6. But row 5 also has a candidate 3 at column 9. That extra home is part of the starting row and cannot be left out of the count.

The full list of possible columns is 2, 3, 4, 6 and 9: five columns, not four. Row 5 could use column 9, leaving one of the four supposed crossing columns without a 3 from these rows. Keep the 3 at the proposed target, row 4, column 6. This is not a basic Jellyfish.

Try it yourself

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

This version rotates and renumbers the first board. Read the darker blue squares in rows 1, 2, 4 and 7, then check the whole length of those rows. Which candidate can their Jellyfish remove from the green-ringed target at row 8, column 8?

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

How to spot it faster

  • Follow one digit at a time. Compare four rows with two to four homes each, and count the different column numbers. They must fit in exactly four columns. Reverse rows and columns to search the other orientation.
  • Count every home on each starting line, including candidates outside the shape you hoped to find. A fifth crossing line breaks a basic Jellyfish.
  • Try smaller patterns first. Two-line X-Wings and three-line Swordfish take less tracking; adding an unrelated row to one of them does not make a useful four-line argument.

Common mistakes

Expecting sixteen candidates

A Jellyfish does not need four homes on every starting line. Two, three or four are allowed. Missing intersections are fine; an extra home outside the four crossing lines is not.

Crossing out the supporting candidates

The removals are outside the starting lines, along the crossing lines. The pattern does not choose among its supporting squares, and those candidates must stay.

Questions

Further reading

Try it

Try an expert 9×9 once simpler moves stop helping. Jellyfish is uncommon, and a random expert deal may use other techniques instead. The worked boards and separate exercise here give you a pattern to study without waiting to encounter one in a game. Free hints still stop at pairs.

Play solo on an expert 9×9