In the

Pure Jellyfish Collection, there were several examples of jellyfish that can be seen in the placement of givens before any pencil marks are entered. If the givens (regardless what digit) in four rows occupy the same four columns (or vice versa), the empty spaces they leave will be in the remaining five rows/columns. If a digit is absent from the 4x4 subset of givens, but present in one of the other rows/columns, the spaces left for candidates of that digit will necessarily be in just four rows and four columns - i.e. a jellyfish.

How useful is it to look for these "instant" jellyfish in a puzzle where you can see a jellyfish shaped space in the givens? I found a pattern in the patterns game with 4 rows having 4 clues each in the same 4 columns, leaving a near-jellyfish-shaped space. How many puzzles had a digit missing from the 4x4 subset of givens, but given elsewhere in the puzzle, making an instant jellyfish? Here are the counts from

patterns game #0052, grouped into ER ranges

(see here for explanation of ER/EP/ED in patterns game):

- Code: Select all
`ER range puzzles instant JF`

1.2-5.0 28 16

5.2-7.9 37 12

8.0-9.5 28 6

In the puzzles where a jellyfish is not required (ER 1.2-5.0) the "instant" jellyfish (appearing in over half the puzzles) would be subsumed by "easier" methods, but it gives a large number (8 or 9) of eliminations right at the beginning for relatively low investment. Where a jellyfish or something more difficult is required (ER >= 5.2) the proportion of puzzles with the instant jellyfish is still pretty high until you get into the very hardest range. In the 10 puzzles where a jellyfish is needed for the first elimination (ED= 5.2), it is easier (IMO) to find the instant jellyfish from the givens than to fish it out of a sea of pencil marks.

I'd be interested to know the frequency of a 4x4 subset of givens in a large database of "typical" puzzles, and what proportion of those have an instant jellyfish.

[edit: fixed hyperlinks - thanks, eleven!]