## Hodoku Franken Fish

This post proposes a spotting technique for Franken Fish, based on the Hodoku’s Mutant Jellyfish example cited earlier in this review. It also shows how Sysudoku fish analysis techniques apply to Franken fish. Finally it reports how pattern analysis surpasses the Franken fish of this example, and how the puzzle can be finished.

Remember Hodoku’s Mutant Jellyfish? It was the Franken Fish into which your strenuous kraken analysis workout poked holes. As Churchill might have said, ignoring Franken Fish is something up with which Sysudoku will not put! So now it’s time to return from our finned fishing haul with a close look at Hodoku’s Franken fish. The adds boxes to lines in the sysudokie tackle box. Does the blank line tally and scratchpad suset enumeration still apply? Can Franken fish actually be spotted with the naked eye (and brain)? Yes and yes.

Here is that Hodoku Mutant Jellyfish, pictured on the X-panel as we have been doing the finned fish. The base set (solid lines) includes the SW box.

This case suggests a spotting rationale. Having noticed the alignment of rows 1,2 and 5 being spoiled by other rows bringing in more columns, we suddenly see the SW box as a cover unit that introduces no more columns

Generally, we want the base to enclose fewer candidates and the cover units to cover many. The SW box adds a base unit for free!

Scratchpad enumeration is very consistent with these objectives. The suset list for rows begins 1/125, 2/128, 3/179, 2/1257, 5/1257, . . .

This quickly yields a multiple finned swordfish 125/1257 . Maybe you’d like to see if it has any victims, but the Franken offers us 9 cover set victims at the small cost of giving up three potential victims in the SW box to the base units.

Hodoku Franken 1 even has a suset prescription. It is 125SW/1257. With the Franken box, it’s still about row positions, i.e. columns..

I’ll have to try this strategy in collection reviews, but I think I’m onto something.

The guiding minimum cover principle applies in the second Hodoku Franken example on the same grid, though not as well, in the column direction. The minimum row count columns 3 and 4 are taken as base units, and the East box for a finned Franken swordfish. Two victims see the fin, one via a grouped forcing chain, which Hodoku misses. As they did in the homework kraken analysis, the minimum columns play a role in the forcing chains saving the other victims by confirming the fin.

Although Hobiger shows little insight into human solving, his batting cage examples have been valuable to the cause.

Patterns are another form of logical restriction remotely related to fish. Starting freeforms from the bottom up, the available patterns leave orphans duplicating the Franken eliminations, plus four more. I’ve added lines and curves in black, to illustrate how freeforms fail to complete, leaving orphans. Lines to the early orphans become dotted curves where the next choice of candidate makes the freeform impossible to complete.

Amazingly, removing all of these orphans does not bring Hodoku’s primary Franken down. Hodoku doesn’t report solutions, so I finished the puzzle as a check to make sure I had not removed a clue. If you want to work through the Franken example from the site diagram, you’ll have to add 5r4c1, 6r6c5, and 8r9c7.

My first find, was the naked triple and SW boxline removals shown here.

From there I added two clusters and found a bridge

!(red & blue) => orange or green

which eliminated 8r6c4 and expanded the blue/green cluster.

I got the solution with a color trial, blue implying orange and deleting all 9’s from c2, an Andrew Stuart Unit Forcing Chain (12/11/12) in reverse.

The solution 8-pattern is the solid red one on the left panel above. On this grid, it starts at the top in green, and finishes at the bottom in red.

The last two Hodoku examples raise more questions than answers about Franken fish as a viable human solving strategy. His Franken Line fin 2-wing is duplicated by s simple box finned 2-wing.

Does the Franken look familiar? A close cousin appeared in my previous post. Hmmmm.

Hodoku’s Franken endo finned 9-wing also falls by a simple freeform pattern analysis.

This encounter with Hodoku dissipated my lingering dread of the Franken fish. It certainly promoted the suset enumeration tool for fish and finned fish, and my case for kraken analysis of all finned fish.

I’m pleased with the role played by freeform pattern analysis as well. On his Last Resorts page, Hodoku dismisses patterns, saying the templates (his patterns) are not meant for human players. Another pronouncement best ignored.

Happy Holidays, everyone. Next week begins the final of this Hodoku marathon review. We enter the finish line stadium with sharpened systematic tools. Now it’s time for the ALS toxic set, a.k.a ALS-XZ, kick.

## About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
This entry was posted in Advanced Solving, Expert Reviews, Hobiger and tagged , , , , . Bookmark the permalink.

### 2 Responses to Hodoku Franken Fish

1. strmckr says:

“Hodoku doesn’t report solutions:”

http://hodoku.sourceforge.net/en/index.php

— Technically it can using its Command prompt functions, since its program uses a forum of dlx to verify that the grid has 1 solution before it applies any of its solving techniques search functions.

— Second method, is that it highlights candidates or solved values that are incorrectly added or removed in a different colour. RED for the most part unless you changed defaults.

“On his Last Resorts page, Hodoku dismisses patterns, saying the templates (his patterns) are not meant for human players. Another pronouncement best ignored.”

Templates – are not “patterns” or fish or anything of that sort they are exactly this.

templates are a physical hard mapped out representation of all possible arrangements of a single digit within an empty grid, recorded as individual “potential ” solutions

with every placement for digit for a “x” you can remove every copy of those potential “solutions” that did not have “x” as a valid location.

those that are left are possible solutions, if you have all these “templates” mapped out you can scan each cell to see if there is a “common” missing cell, that cell will never hold a candidate since its not one of the potential solutions.

– templates
they are literately what I described above and generally should be avoided in manual solving as it requires mapping every possible valid pattern out.

all of hodokus fish are coded using template search space reduction built on the below formula.
{ie if there is a common missing cell, you know all the rows,box,cols holding digits thus u have a list for base/cover and what can/cant be a fin ->> essentially it builds the fish backwards }

Hodoku naturally reduces variation counts on purpose:
it can report all fish types and sizes takes a bit to figure out how to turn that function i warn caution doing so as many thousands of fish can spew forth on a single grid. since each fish as displayed can “morph” multiple different ways for the exact same elimination and increase in size as well !

now as to what Fish really are is found by reading the following link to a well maintained document.

http://forum.enjoysudoku.com/the-ultimate-fish-guide-t4993.html

for additional/ alternative methods on how to spot find fish mathematically or analytically
see this great idea
http://forum.enjoysudoku.com/about-the-arithmetic-of-ultimate-fish-t5256.html

Sets:
Bn = units of the base set
Base (size N): B = B1 + B2 … + BN
Base Intersect: BI = B1*B2 + B1*B3 … + B1*BN + B2*B3 … + (BN-1)*BN

Cn = units of the cover set
Cover (size N): C = C1 + C2 … + CN
Cover Intersect: CI = C1*C2 + C1*C3 … + C1*CN + C2*C3 … + (CN-1)*CN

Hidden Pattern: H = (B \ C) + BI
Exclusion: E = (C \ B) + CI

Symbol Key:
‘+’ union (‘|’ in C++)
‘*’ intersection (‘&’ in C++)
‘\’ substraction (‘X & ~Y’ in C++)

Conjecture:

If the “hidden set” is empty,
then the “exclusion set” is empty also.

1. exclusions in C\B

B will supply the digit N times (not less since none in BI);
all N will be in C (since none in B\C);
this supplies the full quota of the digit for the N units of C,
therefore, exclude it elswhere in C (i.e. in C\B).

2. exclusions in CI

placing the digit in CI would satisfy 2 (or more) units of C,
so C could only take N-1 of the total N supplied by B.

which satisfies:

Logic behind Finned fish based eliminations :

Conjecture:

In an NxN finned fish:
If the Unfinned fish component is false, then at least one of the fins(#) is true
If all the fins are false, then the unfinned fish component is true

Implications:

Only potential eliminations (#) that can be linked to all fins are called eventual eliminations and can be safely eliminated

Proof:

In an NxN finned fish:
1. If the unfinned Fish component is true —->
One vertex(#) per base sector will be true to satisfy the N base sector cover by N sectors —->
Any candidate in the base sectors other than vertices (including all fins) will be false2. If all fins are false —->
we are left with an NxN unfinned fish —->
Unfinned fish component is true

Anway this is long enough post from me, don’t get caught in any nets trying to dive into these waters

strmckr

• Sudent says:

Very informative comment. Thanks very much.

On the template issue, I had already used the word for a resource I send to readers who want to use PowerPoint as I do. So I followed Andrew Stuart’s use of “pattern” to describe templates in the blog. I develop patterns as needed with a graphic tool called a freeform to limit patterns and to find candidates in no pattern. I call them “orphans”. Collectively I call these methods LPO, Limited Pattern Overlay. You should have a look. I use simple freeform pattern analysis on esoteric Hodoku fish in a recent post.

I definitely want to explore the fish finding ideas, but I probably won’t post anything as deep as the forum threads go. From the comment I know you’ll like the adaptation of computer technology in the suset scratchpad tool for enumerating regular fish, finned fish, locked sets and ALS. Could my readers and I have your reaction?

Sudent