Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

Re: Exotic patterns a resume

Postby Leren » Thu Oct 09, 2014 9:54 pm

Hi Danny,

I get the same 15 eliminations for this Exocet because I recognise a second secondary equivalence r4c4==r3c6.

Is it possible to find an example where you can get additional Exocet eliminations that aren't duplicated by a secondary equivalence involving a given/solved cell ?

Leren
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Re: Exotic patterns a resume

Postby daj95376 » Thu Oct 09, 2014 11:34 pm

Leren wrote:Is it possible to find an example where you can get additional Exocet eliminations that aren't duplicated by a secondary equivalence involving a given/solved cell ?

I'm not sure. This example is probably on the border considering the position of 4 and 5 in [r1] and [r3]. However, the logic seems more complex than forming a simple secondary equivalence on 6.

Code: Select all
98.7..6..5...9......45.8.9.8.....3...6..5..4...7.......9..8..6..4..7..5....2....1

 r2  b3  Locked Candidate 1              <> 4    r2c46

 +--------------------------------------------------------------------------------+
 |  9       8       123     |  7       1234    1234    |  6      Q123     5       |
 |  5       1237    123-6   | B136     9      B1236    |  12478   12378   23478   |
 | R6-1237 Q123-7   4       |  5       123-6   8       |  127     9       237     |
 |--------------------------+--------------------------+--------------------------|
 |  8       125     1259    |  1469    1246    124679  |  3       127     2679    |
 |  123     6       1239    |  1389    5       12379   |  12789   4       2789    |
 |  4       123     7       |  13689   1236    12369   |  5       128     2689    |
 |--------------------------+--------------------------+--------------------------|
 |  1237    9       1235    |  134     8       1345    |  247     6       2347    |
 |  123-6   4       12368   |  1369    7       1369    |  289     5       2389    |
 |  37-6    357     3568    |  2       346     34569   |  4789    378     1       |
 +--------------------------------------------------------------------------------+
 # 157 eliminations remain

 ***   value   = <1> true   locks cells true:   r1c8        ( Single-Target cell )
 ***   value   = <2> true   locks cells true:   r1c8        ( Single-Target cell )
 ***   value   = <3> true   locks cells true:   r1c8        ( Single-Target cell )

 ***   value   = <6> true   locks cells true:   r3c1        ( value forced true in base cells and r3c1 )
                                                            ( exists as target cell due to JExocet )

 ### -1236- QExocet   Base = r2c46   Target = r1c8==r3c2,r3c1

 ### -1237- QExocet   Base = r3c79   Target = r1c5==r2c3,r2c2

_
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Re: Exotic patterns a resume

Postby Leren » Fri Oct 10, 2014 12:49 am

No luck this time. For the 1236 Exocet I get 2 secondary equivalences r1c8==r3c2 and r3c1==r1c7 for the same 9 eliminations.

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Re: Exotic patterns a resume

Postby daj95376 » Fri Oct 10, 2014 4:24 am

Leren wrote:No luck this time. For the 1236 Exocet I get 2 secondary equivalences r1c8==r3c2 and r3c1==r1c7 for the same 9 eliminations.

It may be that secondary equivalences are equivalent to the Exocet Single-Target results.

I now have 1,225 JExocet puzzles that also contain Exocet Single-Target patterns where you might not find equivalent secondary equivalences.


[Edit: reduced the puzzle count by discarding puzzles where my secondary equivalences accounted for a single candidate being true.]

_
Last edited by daj95376 on Fri Oct 10, 2014 4:53 pm, edited 3 times in total.
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Re: Exotic patterns a resume

Postby David P Bird » Fri Oct 10, 2014 8:19 am

A digit can't be a member of a JExocet if a) it doesn't comply with the 'S' cell requirement and b) it isn't a candidate in either target. If this is the only fly in the ointment then it's an Almost JExocet.

Code: Select all
 *--------------------------*--------------------------*--------------------------*
 |  9       8       123     |  7       1234    1234    |  6      T123     5       |
 |  5       1237    123-6   | B136     9      B1236    |  12478   12378   23478   |
 |  12367  T1237    4       |  5       123-6   8       |  127     9       237     |
 *--------------------------*--------------------------*--------------------------*
 |  8       125     1259    |  1469    1246    124679  |  3       127     2679    |
 |  123     6       1239    |  1389    5       12379   |  12789   4       2789    |
 |  4       123     7       |  13689   1236    12369   |  5       128     2689    |
 *--------------------------*--------------------------*--------------------------*
 |  1237    9       1235    |  134     8       1345    |  247     6       2347    |
 |  1236    4       12368   |  1369    7       1369    |  289     5       2389    |
 |  367     357     3568    |  2       346     34569   |  4789    378     1       |
 *--------------------------*--------------------------*--------------------------*

In this case either (6)is true in r2c46 or there is an (123)JE:r2c46,r1c8,r3c2.
But the JE is false because there is no base digit in r1c79. Hence (6)r2c46 is true.

[Edits: First post was withdrawn because of a logic error, then replaced with this correction]
Last edited by David P Bird on Fri Oct 10, 2014 9:16 am, edited 2 times in total.
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Re: Exotic patterns a resume

Postby blue » Fri Oct 10, 2014 8:23 am

Hi Leren,

I'm not sure what you're after, exactly, but there are cases like the 2 below.

Code: Select all
+-----------------------+-----------------------+-------------------------+
| 9      8      T134-2  |  7      1345-2  135-2 | 6        134    T2-45   |
| 5      1347-2  134-2  | B124    6      B123   | 13478-2  134789  4789-2 |
| 237    12347   6      |  9      1345-2  8     | 1347-2   1347    457-2  |
+-----------------------+-----------------------+-------------------------+
| 4      156     18     |  3      159     15679 | 178      2       6789   |
| 268    1256    9      |  1246   1245    12567 | 1478     14678   3      |
| 236    1236    7      |  1246   8       1269  | 5        1469    469    |
+-----------------------+-----------------------+-------------------------+
| 1      23679   238    |  268    239     4     | 2378     5       678-2  |
| 2368   2346    5      |  1268   7       1236  | 9        3468    468-2  |
| 23678  234679  2348   |  5      239     2369  | 23478    34678   1      |
+-----------------------+-----------------------+-------------------------+

 ***   value   = <1> true   locks cells true:   r1c3        ( Single-Target cell )
 ***   value   = <3> true   locks cells true:   r1c3        ( Single-Target cell )
 ***   value   = <4> true   locks cells true:   r1c3        ( Single-Target cell )

 ***   value   = <2> true   forced to:  c39 in r1           ( Establishing the
                                                              "dual target" Exocet )

### -1234- Exocet   Base = r2c46   Target = r1c39


Code: Select all
+----------------------+------------------------+----------------------------+
|  9      8      134-2 | 7      6       T134-2  | 5       124       234      |
|  7      6      134-2 | 3489  T2-1389   5      | 134-2   1489-2    3489-2   |
| B123   B124    5     | 3489   1389-2   1348-2 | 1347-2  146789-2  346789-2 |
+----------------------+------------------------+----------------------------+
|  4      1259   1269  | 56     7        16     | 8       3         259      |
|  1568   3      169   | 2      158      1468   | 147     14579     4579     |
|  1258   125    7     | 3458   1358     9      | 6       1245      245      |
+----------------------+------------------------+----------------------------+
|  12356  1245   8     | 356    35-2     7      | 9       2456      23456    |
|  2356   24579  23469 | 1      3589-2   2368   | 2347    245678    2345678  |
|  2356   2579   2369  | 35689  4        2368   | 237     25678     1        |
+----------------------+------------------------+----------------------------+

 ***   value   = <1> true   locks cells true:   r1c6        ( Single-Target cell )
 ***   value   = <3> true   locks cells true:   r1c6        ( Single-Target cell )
 ***   value   = <4> true   locks cells true:   r1c6        ( Single-Target cell )

 ***   value   = <2> true   forced to:  r1c6 or r2c5 in b2  ( Establishing the
                                                              "dual target" Exocet )

### -1234- Exocet   Base = r3c12   Target = r1c6,r2c5
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Re: Exotic patterns a resume

Postby Leren » Fri Oct 10, 2014 9:50 am

Hi blue, my suggestion is that an Exocet Secondary Equivalence involving a given/solved cell might always lead to the same eliminations as does Exocet Single Target Cell logic. This would only be true for Exocet patterns where SE's are possible, which limits them to 3 row (or column) 3 box patterns. In both of Danny's examples there were in fact 2 SEs, so my suggestion may have to be amended to there being 2 SE's in the pattern, at least one of which involves a given/solved cell. I would think that if 2 logical pathways always lead to the same eliminations there should be a way of proving it, or if they don't always do so, a counter-example could be found.

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Re: Exotic patterns a resume

Postby daj95376 » Fri Oct 10, 2014 11:59 am

At the risk of posting yet another puzzle that Leren resolves with secondary equivalences, I'll make this my last attempt.

Code: Select all
98.76.5..7..4..8....6..3.7.87.5..4...2......7.......814...7...8.9..........9...45

   c3b7  Hidden Pair                     =  78   r89c3

 +--------------------------------------------------------------------------------+
 |  9       8       1234    |  7       6       1-2     |  5       123     234     |
 |  7       135     1235    |  4       1259    159-2   |  8       12369   2369    |
 |  15-2    145     6       |  128     12589   3       |  129     7       249     |
 |--------------------------+--------------------------+--------------------------|
 |  8       7       139     |  5       1239    169-2   |  4       2369    2369    |
 |  136     2       1349    |  1368    13489   14689   |  369     5       7       |
 |  356     3456    3459    |  236     2349    7       |  2369    8       1       |
 |--------------------------+--------------------------+--------------------------|
 |  4       1356    135-2   | Q136-2   7      R2-156   |  1369-2  1369-2  8       |
 |  1356-2  9       78      |  1368-2  13458-2 14568-2 |  1367-2 B1236   B236     |
 | R2-136  Q136     78      |  9       138-2   168-2   |  1367-2  4       5       |
 +--------------------------------------------------------------------------------+
 # 152 eliminations remain

 ***   value   = <1> true   locks cells true:   r7c4        ( Single-Target cell )
 ***   value   = <3> true   locks cells true:   r7c4        ( Single-Target cell )
 ***   value   = <6> true   locks cells true:   r7c4        ( Single-Target cell )

 ***   value   = <2> true   locks cells true:   r9c1        ( value forced true in base cells and r9c1==r7c6 )
                                                            ( exists as target cell due to JExocet )

 ### -1236- QExocet   Base = r8c89   Target = r7c4==r9c2,r9c1==r7c6

Note: besides Basics following these eliminations, there's also an X-Wing for 2.


Addendum

Details for anyone who might wonder how the Exocet Single-Target patterns exist.


Code: Select all
 r8c8=1; r3c7=1; JellyFish r147c1\c36b57  w/fin cells = r5c1,r7c4  -> -1r5c4  =>  =1r7c4
 +-----------------------------------+
 |  .  .  1  |  .  .  1  |  . ~1  .  |
 |  .  1  1  |  .  1  1  |  . ~1  .  |
 | -1 -1  .  | -1 -1  .  | =1  .  .  |
 |-----------+-----------+-----------|
 |  .  .  1  |  .  1  1  |  .  .  .  |
 |  1  .  1  |  1  1  1  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  .  1  |
 |-----------+-----------+-----------|
 |  .  1  1  | Q1  . R1  | ~1 ~1  .  |
 | ~1  .  .  | ~1 ~1 ~1  | ~1 B1  .  |
 | R1 Q1  .  |  .  1  1  | ~1  .  .  |
 +-----------------------------------+

Code: Select all
 r8c89=2; SwordFish c347\r367  w/fin cells = r12c3  -> -2r3c1  =>  =2r9c1
 +-----------------------------------+
 |  .  .  2  |  .  .  2  |  .  2  2  |
 |  .  .  2  |  .  2  2  |  .  2  2  |
 |  2  .  .  |  2  2  .  |  2  .  2  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  2  2  |  .  2  2  |
 |  .  2  .  |  .  .  .  |  .  .  .  |
 |  .  .  .  |  2  2  .  |  2  .  .  |
 |-----------+-----------+-----------|
 |  .  .  2  | Q2  . R2  | ~2 ~2  .  |
 | ~2  .  .  | ~2 ~2 ~2  | ~2 B2 B2  |
 | R2  .  .  |  .  2  2  | ~2  .  .  |
 +-----------------------------------+

Code: Select all
 r8c89=3; SwordFish c157\r569  w/fin cell = r4c5  -> -3r56c4  =>  =3r7c4
 +-----------------------------------+
 |  .  .  3  |  .  .  .  |  .  3  3  |
 |  .  3  3  |  .  .  .  |  .  3  3  |
 |  .  .  .  |  .  .  3  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  3  |  .  3  .  |  .  3  3  |
 |  3  .  3  |  3  3  .  |  3  .  .  |
 |  3  3  3  |  3  3  .  |  3  .  .  |
 |-----------+-----------+-----------|
 |  .  3  3  | B3  .  .  | ~3 ~3  .  |
 | ~3  .  .  | ~3 ~3  .  | ~3 B3 B3  |
 | R3 Q3  .  |  .  3  .  | ~3  .  .  |
 +-----------------------------------+

Code: Select all
 r8c89=6; X-Wing r28\c89 - r4c89 = r4c6 - r79c6  =>  =6r7c4
 +-----------------------------------+
 |  .  .  .  |  .  6  .  |  .  .  .  |
 |  .  .  .  |  .  .  .  |  .  6  6  |
 |  .  .  6  |  .  .  .  |  .  .  .  |
 |-----------+-----------+-----------|
 |  .  .  .  |  .  .  6  |  .  6  6  |
 |  6  .  .  |  6  .  6  |  6  .  .  |
 |  6  6  .  |  6  .  .  |  6  .  .  |
 |-----------+-----------+-----------|
 |  .  6  .  | Q6  . R6  | ~6 ~6  .  |
 | ~6  .  .  | ~6  . ~6  | ~6 B6 B6  |
 | R6 Q6  .  |  .  .  6  | ~6  .  .  |
 +-----------------------------------+

_
Last edited by daj95376 on Wed Oct 22, 2014 8:02 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby Leren » Fri Oct 10, 2014 8:55 pm

Hi Danny, I see the same 2 SE's as you but neither is to a given/solved cell - so only 3 eliminations.

Well done ! I think I'm more relieved than you are :) .

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Re: Exotic patterns a resume

Postby David P Bird » Sun Jan 25, 2015 5:30 pm

In writing up the decriptions of JExocets in its various forms I've met this theoretical situation:

The candidates in the base cells are (abcd)
The number of cover houses needed to cover the 'S' cells for each digit are (a)=2, (b)=2, (c)=3, (d)=1
This would allow (d) to occupy both target cells if it was paired with (c), and obviously other two digit combinations out of (abc) would also be possible.

Does anyone feel inclined to run a computer search for one of these flying fish?
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Re: Exotic patterns a resume

Postby daj95376 » Sun Jan 25, 2015 8:55 pm

[Withdrawn: working from an incorrect understanding of the JExocet properties.]
Last edited by daj95376 on Wed Jan 28, 2015 1:15 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby David P Bird » Sun Jan 25, 2015 11:22 pm

Withdrawn - response to DAJ
Last edited by David P Bird on Wed Jan 28, 2015 9:24 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby daj95376 » Mon Jan 26, 2015 8:26 am

[Withdrawn: working from an incorrect understanding of the JExocet properties.]
Last edited by daj95376 on Wed Jan 28, 2015 1:15 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby David P Bird » Mon Jan 26, 2015 10:55 am

Withdrawn - response to DAJ
Last edited by David P Bird on Wed Jan 28, 2015 9:25 pm, edited 1 time in total.
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Re: Exotic patterns a resume

Postby daj95376 » Mon Jan 26, 2015 7:36 pm

[Withdrawn: working from an incorrect understanding of the JExocet properties.]
Last edited by daj95376 on Wed Jan 28, 2015 1:16 pm, edited 1 time in total.
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