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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Tue Apr 10, 2012 6:02 am Post subject: au tough 4/10/12 |
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| Code: |
*-----------*
|9..|7..|...|
|...|.42|5.6|
|...|..1|87.|
|---+---+---|
|...|...|15.|
|...|.3.|...|
|.56|...|...|
|---+---+---|
|.21|8..|...|
|3.9|52.|...|
|...|..7|..4|
*-----------* |
Play/print online |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Apr 10, 2012 6:36 pm Post subject: |
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I threw in the towel. There's one Finned X-Wing on 7 that looks worthless. 
| Code: |
+-------------------+----------------+-------------------+
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 | 39 4 2 | 5 139 6 |
| 2456 346 2345 | 369 569 1 | 8 7 239 |
+-------------------+----------------+-------------------+
| 2478 34789 23478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 2478 | 1249 3 5 | 24679 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 23479 23489 23789 |
+-------------------+----------------+-------------------+
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 568 68 58 | 139 19 7 | 239 239 4 |
+-------------------+----------------+-------------------+
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Play this puzzle online at the Daily Sudoku site |
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SudoQ
Joined: 02 Aug 2011
Posts: 127
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| Posted: Tue Apr 10, 2012 7:02 pm Post subject: |
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I tested this puzzle in a public solution program, and it found a 'Sue de Coq': | Code: | | r1c23 - {12356} (r1c789 - {1234}, r3c1 - {56}) => r3c2<>6, r3c3<>5, r1c6<>3 |
At some point I'll try to understand how such a thing works!
/SudoQ |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Apr 10, 2012 7:20 pm Post subject: |
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| Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 1-39 19 7 | 239 239 4 |
*--------------------------------------------------------------------*
np[(3=9)r2c4-anp(9=356)r3c145] => r9c4<>39
stte
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I hope I'm showing this correctly.
if r2c4=9 r3c15 become a 56 pair making r3c4=3
this makes r23c4 a Pseudo 39 pair and therefore r9c4<>39
oops what if it is a 3!
back to the drawing board...it look so good this morning.
r9c4 <> 3 only but that is all that is needed,
(3=9)r2c4-anp(9=356)r3c145 => r9c4<>3
Play/print online |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Apr 10, 2012 7:49 pm Post subject: |
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| arkietech wrote: | | Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 1-39 19 7 | 239 239 4 |
*--------------------------------------------------------------------*
np[(3=9)r2c4-anp(9=356)r3c145] => r9c4<>39
stte
|
I hope I'm showing this correctly.
if r2c4=9 r3c15 become a 56 pair making r3c4=3
this makes r23c4 a Pseudo 39 pair and therefore r9c4<>39
oops what if it is a 3!
back to the drawing board...it look so good this morning.
r9c4 <> 3 only but that is all that is needed,
(3=9)r2c4-anp(9=356)r3c145 => r9c4<>3
Play/print online |
Nice spot! That's an ALS-xz, by the way. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Apr 10, 2012 10:01 pm Post subject: |
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| arkietech wrote: | | Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 1-39 19 7 | 239 239 4 |
*--------------------------------------------------------------------*
np[(3=9)r2c4-anp(9=356)r3c145] => r9c4<>39
stte
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I hope I'm showing this correctly.
if r2c4=9 r3c15 become a 56 pair making r3c4=3
this makes r23c4 a Pseudo 39 pair and therefore r9c4<>39
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I don't think the r9c4<>39 is correct. My solver reports:
| Code: | (3=9)r2c4 - (9=ALS=3)r3c45 - loop => r1c6<>3
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But it has a bug and missed r9c4<>3 as well. It also doesn't list the ALS connecting cell -- r3c1 -- in its most compact output format.
I also have a problem with ALS loops and the "passive digits" -- <56> -- performing eliminations. I nearly fell out of my chair the first time I saw Luke use them in one of his solutions. _  _
A more accurate representation:
| Code: | (3=9)r2c4 - (956=ALS=563)r3c145 - loop => r1c6,r9c4<>3, r3c3<>5, r3c2<>6
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Regards, Danny |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Apr 11, 2012 1:42 am Post subject: |
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| Luke451 wrote: |
Nice spot! That's an ALS-xz, by the way. |
Here is what I see: | Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 19-3 19 7 | 239 239 4 |
*--------------------------------------------------------------------*
(3=9)r2c4-(9=3np[56])r3c145 => r9c4<>3 |
I don't see the ALS-xz  |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Apr 11, 2012 4:08 pm Post subject: |
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| arkietech wrote: | | Luke451 wrote: |
Nice spot! That's an ALS-xz, by the way. |
Here is what I see: | Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 19-3 19 7 | 239 239 4 |
*--------------------------------------------------------------------*
(3=9)r2c4-(9=3np[56])r3c145 => r9c4<>3 |
I don't see the ALS-xz |
There are different ways of looking at this, but now I think that it is not only an ALS-xz, but a doubly-linked ALS-xz! Both the 3 and 9 are "restricted common digits." That carries a little more clout that just an ALS-xz as far as the number of eliminations.
I'm rusty on doubly-linked ALS-xz, and I'm away from my notes. Will follow up...
For now, here's one ALS-xz argument:
| Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 19-3 19 7 | 239 239 4 |
*--------------------------------------------------------------------* |
A: (39)r2c4
B: (3569)r3c145
x=9 (restricted common)
z=3 (other common)
==>r9c4<>3
In Eureka: (3=9)r2c4-(9=356)als:r3c145 ==>r9c4<>3 |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Apr 11, 2012 4:24 pm Post subject: |
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| Luke451 wrote: | A: (39)r2c4
B: (3569)r3c145
x=9 (restricted common)
z=3 (other common)
==>r9c4<3>r9c4<>3 |
Thanks Luke451  A set in a single cell is what was throwing me.
Looking forward to more on ALS's The Eureka helps. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Apr 11, 2012 6:58 pm Post subject: |
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| daj95376 wrote: | | Code: | | (3=9)r2c4 - (956=ALS=563)r3c145 - loop => r1c6,r9c4<>3, r3c3<>5, r3c2<>6 |
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After seeing this, I'm quite convinced this is indeed a doubly-linked ALS-xz.
As I mentioned above, both the (3) and (9) are "restricted common candidates." This simply means that the (3) cannot be in both sets (39) and (3569) at the same time, and the (9) cannot be in both sets at the same time.
"Extra digits" are those candidates in both sets that are not RCCs (restricted common candidates.)
There are no extra digits in the (39) set, but the (3569) set has the extra digits (56).
| Code: | *--------------------------------------------------------------------*
| 9 136 235 | 7 568 368 | 234 1234 123 |
| 178 1378 378 |a39 4 2 | 5 139 6 |
|b56 346 2345 |b369 b569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 19-3 19 7 | 239 239 4 |
*--------------------------------------------------------------------* |
The eliminations are any outside digits that can see all the candidates of either RCC, and all the outside candidates that can see all of the extra digits:
* (3)r9c4 and (3)r1c6 both see both the RCC (3) and are out.
* (6)r3c2 and (5)r3c3 both see all of the extra digits (56) and are out.
Those are the same eliminations as the loop your solver found, Danny. They also show how doubly-linked turns "passive digits" into passive aggressive.
I would say the doubly-linked ALS-xz has the slight advantage over the loop in that utilizing it does not require any chain whatsover. Pattern solvers can immediately make the elims as soon as the pattern is recognized. Instant gratification 
(Edit: corrected terminology, RCC is correct, not RCD)
Last edited by Luke451 on Fri Apr 13, 2012 8:29 pm; edited 1 time in total |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Fri Apr 13, 2012 5:38 pm Post subject: |
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| SudoQ wrote: | I tested this puzzle in a public solution program, and it found a 'Sue de Coq': | Code: | | r1c23 - {12356} (r1c789 - {1234}, r3c1 - {56}) => r3c2<>6, r3c3<>5, r1c6<>3 |
At some point I'll try to understand how such a thing works! |
How about the doubly-linked ALS-xz perspective, as long the topic came up?
Your Sue de Coq is a complement of the doubly-linked ALS-xz pointed out above.
| Code: | *--------------------------------------------------------------------*
| 9 *136 *235 | 7 568 -368 |*234 *1234 *123 |
| 178 1378 378 | 39 4 2 | 5 139 6 |
|#56 34-6 234-5 | 369 569 1 | 8 7 239 |
|----------------------+----------------------+----------------------|
| 2478 34789 3478 | 2469 6789 689 | 1 5 2789 |
| 12478 14789 478 | 1249 3 5 | 2469 24689 2789 |
| 12478 5 6 | 1249 1789 89 | 2349 23489 23789 |
|----------------------+----------------------+----------------------|
| 47 2 1 | 8 69 3469 | 3679 369 5 |
| 3 47 9 | 5 2 46 | 67 18 18 |
| 56 68 58 | 139 19 7 | 239 239 4 |
*--------------------------------------------------------------------* |
* In row 1 there is an almost locked set (6 digits in 5 cells), (123456)r1c23789
# In r3c1 there is a second ALS (2 digits in 1 cell), (56)r3c1
The two ALSs have two candidates that cannot be in both sets, (5) and (6) (restricted common candidates.)
(5)r3c3 sees both the RCC(5) and can be eliminated.
(6)r3c2 sees both the RCC(6) and can be eliminated.
(3)r1c6 sees every (3) in the first ALS and can be eliminated.
The eliminations are possible because if any digit of an ALS is removed, the set becomes locked.
With the two sets doubly-linked, this would result in too few candidates for the available cells.
Some basics:
A "locked set" exists when N digits are locked in N cells within a house, such as
1 digit in 1 cell
2 digits in 2 cells
3 digits in 3 cells
4 digits in 4 cells
etc.
An "almost locked set" (ALS) exists when N+1 digits are locked in N cells within a house, such as
2 digits in 1 cell
3 digits in 2 cells
4 digits in 3 cells
5 digits in 4 cells
etc. |
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