## Suset Sashimi

This review of Hanson’s Sudoku Assistant shows that his grid ALS discovery algorithm, which I have long used as a scratchpad algorithm for human solvers, is very good at finding effective finned fish and kraken fish, particularly sashimi. Readers were invited to analyze six remaining grid ALS examples from his SA report , using the suset scratchpad algorithm, for checkpoint in this post.

The previous post ended with Bob’s second grid ALS example, a column finned swordfish sporting three box fin victims. Bob’s ALS combines susets 3/79, 6/278, and 9/2789 to form the suset 369/2789. Five potential kraken victims escape by not seeing the fin.

You may have constructed the ALS bottom up, like I did, reaching suset 39/279 for a kraken 8-wing. The victims are all kraken, and the escapees are different.

Or you may have gone to rows with suset 14/458, and let them all get away. Sorry, every suset is not guaranteed to work.

Bob’s third example below is coded as “A 1s”, a link on his site bringing it up on Sudoku Assistant.   The column suset list includes 1/16, 4/17, 9/367. I started with 14/167, and duplicated his removal, 6r6c8, with no kraken victims.

The kraken forcing chain has 6r6c8 seeing the fin, and that is normal enough, but then this victim joins the three escaping candidates on a path verifying the fin. So the real reason for removing 6r6c8 is that it forces another candidate true and false, hence the diamond.

For some reason, SA chooses the larger column ALS, 149/1367. Now the example is cooked more thoroughly, as four candidates in r6 force both 6-candidates out of r9.

Now for the four “outside” examples that Bob collected to show grid ALS at work.

From the collection impossible520, #237, with an ALS list of

16/258, 18/358, 58/357, 69/248

Bob picks 69/248.

The kraken victim also forces both 4 candidates from c1.

In his next impossible520 selection #202, Bob identifies 4r5c5 as the guilty party for removing all 4 candidates from c4, via column ALS 79/358. The sashimi kraken analysis finds all three Cr5 potential victims guilty, confirming 4r5c7.

Bob’s third impossible520, #121, provides a host of grid ALS and several versions of the truth. From a list of 17/159, 34/257, 39/247, 47/259, SA picks 27/259, and then banishes 4c2c3 because it forces c3 to 5 and 7 to 59 and therefore to 9, thereby forcing both 4-candidates from c1, a unit(c1) forcing chain removal. My question is, why r2c3? We can’t do that analysis for every candidate. 4r7c9 forces c7 to 5 and c4 to 25 and therefore to 2. So now we can look for the damage that 4r5c7 and 4r2c4 can do? It’s not humanly practical.

So now make the same suset selection and consider it to describe the sashimi 4-wing with fin at r9c7. Two candidates are now singled out for examination, as potential victims. 4r5c5 escapes because it confirms the fin. Bob’s victim, 4r2c3 is removed because it sees the fin, or if you notice that it also has a forcing chain that confirms the fin, it is removed because the fin has to be true or false. It is an Andrew Stuart digit forcing chain, or more simply, the removal of an almost nice loop.

But wait, the suset 47/259 describes two distinct sashimi 4-wings, depending on which row holds the fin.

Place the fin in r2 and 4r9c1 replaces r3c3 as a potential victim. It does see the fin, and is dismissed, but also because it verifies the fin by a different path, completing an ANL that removes it. The other potential victim, 4r5c5 escapes again, by confirming the new fin.

Bob’s last grid ALS example uses a row based suset 29/134, but he mentions only row 1 to point out the counter clockwise inference path that completes the removal of both 6-candidates from r2. Remember my posting that sashimi wings are skyscrapers? More reliable signposts to this removal are the 6-chain skyscraper or the simple 6-chain ANL.

But failing these, suset 29/134’s sashimi wing would uncover it (below), bringing along with it two kraken suspects to be questioned and released.

In closing this exceptionally long post, I commend you on your patience, and say that Bob’s examples, though incompletely represented in his report, do confirm the power of his grid ALS concept and confirm our admiration for his independent Sudoku thinking. I’ll be getting out my scratchpad in x-panel analysis to seek the sashimi among the thin lines.

But that isn’t all. Stay tuned.