## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

This condenses some of the discussion in <this thread> with a few further observations.

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`      v   v       v           *-------*-------*-------*| b b . | . . . | . . . |     b = base cell restricted to digits from [abc] or [abcd]| . . . | / . . | t . . |     t = target cell (at first will contain every base digit)| . . . | t . . | / . . |     / = companion empty cell unable to hold any base digit *-------*-------*-------*     v = cross line pointers`

In reference to this pattern, a three step system for recognising one-band Exocets is:
1: Find two base cells in a mini-line.
2: Look for two companion empty cells in the other two boxes in the two other lines.
3: Check that in the 3 cross lines each base digit is confined to 2 rows in the 2 parallel bands.

When this pattern is found, the two target cells will eventually reduce to different base digits making non-member digits false in these cells. Later, when a digit is assigned to either target cell, the cross lines will contain a Swordfish for that digit.

This search method works at any puzzle solving stage, but relying on the target cells to hold all the base digits will fail if one of them has previously been eliminated.

Theoretically there are two corollaries:
1: A digit eliminated from both the target cells must be false in the base cells.
2: A pair of digits excluded from the same target cell cannot both be true in the base cells.
The chances of either of these circumstances occurring in a puzzle requiring exotic patterns must be very small though.

Noting that the member digits of a one-band Exocet can't exist as givens elsewhere in the band can aid searching. It also severely reduces the chances of finding a double Exocet with different members.

There may also be prospects for finding Almost Exocets where one of the required conditions is not quite satisfied.

DPB
David P Bird
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### Re: Comments on One-band Exocets

David P Bird wrote:This condenses some of the discussion in <this thread> with a few further observations.

Noting that the member digits of a one-band Exocet can't exist as givens elsewhere in the band can aid searching. It also severely reduces the chances of finding a double Exocet with different members.

There may also be prospects for finding Almost Exocets where one of the required conditions is not quite satisfied.

DPB

Nothing to object to that post.

regarding double exocet, they are of interest if they share the same digit, which is happily the case in all examples i have seen.

I have nearly finished the solution of a puzzle rated 11.5 having both an exocet and a SK loop

It will be part of post 4 and should be published to morrow.

I find that path has interesting things especially regarding effect of "linked UR's" that have often a key role with exocet patterns.

Coding the detection of that first pattern for exocets is still in my target for April, but I have other duties and i am could have to postpone it.

champagne
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### Re: Exotic patterns a resume

An "exocet with a bonus" ???

An unclued r1c3 is one of two or three impediments to a 2-row/2-col 4-digit 4-fish of 0-rank. The addition of two truths with AALS r5c46 provides enough "oomph" to produce a few exclusions. Note the equivalence of r5c46 and [r4c9,r6c3] in the solution.

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`....5...94..1...3..6.7..1....59......8..7.......5.2..73......6...8.9...2.1....4.. 2051;elev;1452 ED=11.2/11.2/9.9     17 Truths = {1R8 346R18 1346C39 5N46}     27 Links = {1346r5 346c4 1346c6 156n3 18n4 18n6 45n9 1b9 3b19 4b37 6b37}     6 Eliminations --> r8c6<>57, r4c9<>8, r6c3<>9, r7c2<>4, r9c1<>6`

____
Clickable thumbnail

[edit: removed redundant truth 1R1]
Last edited by ronk on Thu May 03, 2012 11:42 am, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

Nice one ronk! This puzzle gives us an Almost Exocet that can be embedded in an AIC:

(9)r6c3 - (279=3)r1c2,r23c9 - (3)r1c3 = (1346)Exocet:r5c46,r4c9,r6c3 - (9)r6c3 => r6c3 <> 9

We have an Exocet if r5c46 <> 3 or r1c3 <> 3, and there must be more out there like this one.

I can't see any other AICs though, maybe tomorrow.
David P Bird
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### Re: Exotic patterns a resume

i entered in post 5 some comments on "how to process a sk loop"

. a complete solution to a puzzle having sk loop + exocet
. a link to an old complete solution of Easter Monster

champagne
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### Re: Exotic patterns a resume

The "exocet" definition should be expanded a bit or, depending upon one's POV, the requirements relaxed a bit. Below is the exocet in Golden Nugget and a only-slightly-different pattern in GP-kz0 (morphed).

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`.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... # Golden Nugget.5.....392.......5..3.5.8....2.9...8.7...26..1..4.......6.3..8..2.7.....4....1... # GP-kz0 morph . . . | . . . | . 3 9                . 5 . | . . . | . 3 9 . . . | . . 1 | . . 5                2 . . | . . . | . . 5 . . 3 | . 5 . | 8 . .                . . 3 | . 5 . | 8 . .-------+-------+-------              -------+-------+------- . . 8 | . 9 . | . . 6                . . 2 | . 9 . | . . 8 . 7 . | . . 2 | . . .                . 7 . | . . 2 | 6 . . 1 . . | 4 . . | . . .                1 . . | 4 . . | . . .-------+-------+-------              -------+-------+------- . . 9 | . 8 . | . 5 .                . . 6 | . 3 . | . 8 . . 2 . | . . . | 6 . .                . 2 . | 7 . . | . . . 4 . . | 7 . . | . . .                4 . . | . . 1 | . . .     Golden Nugget                        GP-kz0 morph`

In each case, the pattern digits are <1247>. Note that a pattern digit exists in mini-row r4b4 for GP-kz0, but not for GN. This leaves only three of the four pattern digits at r4c8, and degenerates one of the ususal four "swordfish", but doesn't really reduce the power of the pattern.

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`For the morphed GP-kz0:     13 Truths = {1247R3 147R4 1247R7 12N7}     17 Links = {7c1 14c2 12c4 47c6 1247c7 4n8 7n9 1247b3}`
ronk
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### Re: Exotic patterns a resume

ronk, you've made the same point as me in my 'Comments on One-band Exocets' post aboveâ€“ namely it doesn't matter if the target cells don't hold all the member digits, it's their companion empty cells that are key.
David P Bird
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### Re: Exotic patterns a resume

David P Bird wrote:ronk, you've made the same point as me in my 'Comments on One-band Exocets' post aboveâ€“ namely it doesn't matter if the target cells don't hold all the member digits, it's their companion empty cells that are key.

Hi ronk an david,

The definition as such does not require that both cells of the target are filled with all digits, but it's true that I added that constraint in my old solver to limit the search.

So my old solver does not recognise the exocet in the second pattern.

I'll think of adjustments in the new process to cover all situations of value shown here.

So the problem is not that much to change the definition, but to extend the search.

champagne
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### Re: Exotic patterns a resume

David P Bird wrote:you've made the same point as me in my 'Comments on One-band Exocets' post aboveâ€“ namely it doesn't matter if the target cells don't hold all the member digits, it's their companion empty cells that are key.

So I see, but I think your description would make my example an "almost exocet." I'm saying it should be considered an exocet, meaning there are optional candidates (ala denis_berthier here) for the pattern in the initial pencilmarks.

BTW I often lose concentration after seeing the target cell term.
ronk
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### Re: Exotic patterns a resume

ronk, when a pattern is notated it should really identify all the required elements that are satisfied, but we donâ€™t do that, we show enough elements to enable the reader to check the rest.

In the case of Exocets, champagne has got us all used to using the base cells and the target cells and signposts to the rest of the pattern, and I'm happy to go along with that. However after identifying the base cells and the digit set, the required elements aren't the target cells but their companion empty cells plus the part Swordfish for each of the member digits in the cross lines in the parallel bands. It's when one of those requirements isn't completely satisfied that it becomes an Almost Exocet.

Experience shows us that as soon as we set some notation norm, pretty soon some other alternative seems to win the day, and I'm past fighting over such things.
David P Bird
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### Re: Exotic patterns a resume

ronk wrote:So I see, but I think your description would make my example an "almost exocet."

This is a pure exocet. The logic never requested to have all digits in each of the "target cells" (I have no other word for that)

The only constraint is that any digit in the base needs the target to have a valid permutation.

champagne
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### Re: Exotic patterns a resume

champagne wrote:
ronk wrote:So I see, but I think [edit: David P Bird's] description would make my example an "almost exocet."
This is a pure exocet.

I obviously agree, but then why is GP;kz0 ("GP-kz0") in your "03 NN" file?

[edit1: Also, is daj95376's guess here really the reason "elev-567" is in this file too?]

BTW I think using the semicolon will cause problems with this forum's search utility. [edit2: Hmm, the dash may be no better.]
Last edited by ronk on Sat Apr 07, 2012 3:02 pm, edited 1 time in total.
ronk
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### Re: Exotic patterns a resume

ronk wrote:[

I obviously agree, but then why is GP;kz0 ("GP-kz0") in your "03 NN" file?

just due to the fact that my solver did not detect it as I explained earlier
We have the same with all multi fish patterns not recognised by the solver

champagne
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### Re: Exotic patterns a resume

champagne wrote:
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`sets2789R2 2789R4 2789R5 2789R7 linksets89C2 79C6 79C8 28C9 r2c4 r2c5 r4c3 r4c5 r5c1 r5c7 r7c1 r7c3`

Is there a reason you can't use Allan Barker's format? With his format, readers could simply cut and paste the puzzle (or pencilmarks) and the logic set. To do this, the above would need to look like:

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`     16 Truths = {2R2457 7R2457 8R2457 9R2457}     17 Links = {2c9 7c68 8c29 9c268 57n1 47n3 2n4 24n5 5n7 8b7}`

While there is some flexibility in the format, AFAIK the minimum requirements are:
1. Truths and Links lists separately enclosed in braces, "{ ...... }",
2. 'n' and 'N' for Truth and Link cells, respectively; for example, 2n4 for link r2c4 above ,
3. upper case 'R', 'C, and 'N' in Truths,
4. lower case 'r, 'c, and 'n' in Links.
You're already mostly doing 3) and 4). If it's OK with you and you start using this Xsudo syntax, I can help out by changing the syntax in your existing posts of this thread. I would simply copy and paste the logic set from Xsudo itself. Let me know.
ronk
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### Re: Exotic patterns a resume

ronk wrote:The "exocet" definition should be expanded a bit or, depending upon one's POV, the requirements relaxed a bit. Below is the exocet in Golden Nugget and a only-slightly-different pattern in GP-kz0 (morphed).

After reading some recent posts on Exocet puzzles, I'm testing the following Exocet logic.

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`1)  Select possible base and target cells (using template solver output).2)  For each value in the base cells, use coloring to logically perform:2a) Assume value is true in base cells and perform eliminations.2b) Perform all resulting Hidden Singles for this value.2c) Derive an X-Chain (possibly grouped SI's) from one target cell to the other target cell.    (David's two given/solved cells become important here.)3)  Exocet!`

[Edit: removed specific example.]
Last edited by daj95376 on Sun Apr 08, 2012 2:47 pm, edited 1 time in total.
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