SudoCue Users

time to learn some new techniques, I guess.

Ruud, what ones do you need to solve this one?

Laura

Hi Laura,

Time to brush up those old techniques, I'd say.

This one requires naked & hidden subsets (lots), X-Wing, remote pairs and one colouring step.

It is a very nasty one. There is a chain of 18 forced steps before it breaks.

Ruud.

Perhaps I have muddled up the puzzles. It wouldn't be the first time.

It seemed to me that the first step was to eliminate 7 from r1c3 using the finned swordfish on rows 3, 5 and 9. The only remaining admissible entry for that cell is 2 and the rest seemed elementary.

Steve

Steve wrote:It seemed to me that the first step was to eliminate 7 from r1c3 using the finned swordfish on rows 3, 5 and 9.

I could not discover a finned swordfish in these rows, but there is a 3-chain multicolour opportunity in the 7-pattern.

You used the heavy tool first and missed all the fun!

Ruud.

Ruud

Maybe it’s my fish that are muddled.

Do not the cells marked F form a swordfish with fin r3c1, so eliminating 7 from the cell marked X? Even if they don’t, one of r9c68 must contain 7 and chasing round the F’s makes the elimination anyway – I suspect this may be the colouring to which you referred.

If some cells were not already constrained, the full fish would be: Here the fin is r3c123

I apologise if I have spoiled the fun but I still rate the score Laura 15 Ruud love!

Steve

Hi, Steve! Thanks for explaining the "finned" swordfish. I didn't spot that as quickly as you did, but I did find the same pattern in the "7"s after just a little bit of work.

1. r9c6 = 2 (sole candidate); hidden triplet {1, 8, 9} in bottom center 3x3 box.
2. The "3" in row 2 lies in top left 3x3 box.
3. Hidden pair {1, 9} in row 1; triplet {1, 6, 9} in top center 3x3 box.
4. Hidden pairs {4, 5} and {2, 7} in top center 3x3 box.
5. Pairs {3, 8} and {6, 9} in row 2; triplet {2, 4, 7} in row 3.
6. r1c2 = 5 (unique horizontal)
7. The "6" in column 5 lies in middle center 3x3 box; r4c6 = 8 (sole candidate).
8. Pair {1, 9} in column 5; r8c5 = 8 (sole candidate)
9. The "6" in row 8 lies in bottom right 3x3 box.

Now we're ready for the final blow ...
There are two binary chains in the "7"s, marked +/- and =/~ in the grid above. Since there's a + opposite both an = and a ~, we conclude that r1c3, r3c5. r4c1, r7c4, and r9c8 are not "7", and that r1c4, r3c1, and r9c5 are equal to 7. That's enough to blow it wide open. dcb

You are absolutely right about the Swordfish, Steve.

I did not see it because the candidate in r3c3 was disabled. This is what MJ calls the Sashimi variation?

This puzzle could be a good example in the optimal solving path discussions. In stead of peeling off candidate after candidate, just give it a whack with the biggest tool you've got.

Ruud.

Ruud

Yes, this is MO’s Sashimi observation, which is that a finned swordfish, unlike a proper one, does not necessarily degenerate if based on a 2-2-1 pattern. I think this means that, if you rub out the fin, 2-2-1 remains. This is the case here except that, reading downwards, the pattern without the fin is 1-2-2. However, I do not find this observation easy to understand or precise enough to be helpful in use.

As far as I can make out it is only necessary to follow the swordfish pattern. Thus, on rows, you still look for three rows, with three cells in each neatly lined up in columns, but keep the mental reservation that for one vertex only you may replace the word “cell” with “one, two or three cells lined up in a box.” This makes the finned variety a little easier to spot but it goes further than that. The cells must still line up in columns (with the understanding that one line-up means a column must intersect the box containing the fin) and it must still be the case that there are at least two empty cells in each row so positioned that each pair of rows defines three columns (same understanding required here). This means applying effectively the same test for degeneracy as in the normal case.

I believe that exactly the same principles apply to any m x m fish, which raises the possibility that there might be a use for a squirmbag in a 9 x 9 puzzle after all.

David

I can only admire your facility with chains, being just about able to follow them.

By chance, following these two brought out a curiosity to light. There is another finned swordfish for 7, also present in the starting grid, based on columns 3, 4 and 9. This one eliminates 7 from r4c1, so forcing it into r3c1.

Steve