## Instant Jellyfish Gratification

Everything about Sudoku that doesn't fit in one of the other sections

### Instant Jellyfish Gratification

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 JF1.2-5.0         28      165.2-7.9         37      128.0-9.5         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!]
Last edited by susume on Thu Oct 30, 2008 11:44 pm, edited 2 times in total.
susume

Posts: 19
Joined: 03 August 2008

### Re: Instant Jellyfish Gratification

susume wrote: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.
This observation is very nice. I dont even like to look for swordfish, the better it is for me, that i now can find a jellyfish without pencilmarks in such puzzles with givens in a jellyfish pattern.