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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Mon Jan 21, 2013 10:25 pm Post subject: Vanhegan extreme |
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This is puzzle 6-764603, rated 1.0.1.1.1. This is representative of the type of puzzle that gives me fits. All I've been able to do is a useless X-Wing on 6 and Finned X-Wing on 1.
| Code: |
+--------------+------------------+---------------+
| 3 789 4 | 1258 578 178 | 1279 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
+--------------+------------------+---------------+
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 679 789 |
| 689 5 3 | 7 4 689 | 289 269 1 |
+--------------+------------------+---------------+
| 2 3789 1 | 589 35678 6789 | 789 4 789 |
| 89 6 789 | 1489 2 14789 | 1789 3 5 |
| 4 3789 5 | 89 378 1789 | 6 179 2 |
+--------------+------------------+---------------+
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Play this puzzle online at the Daily Sudoku site |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Jan 22, 2013 1:08 am Post subject: Re: Vanhegan extreme |
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| Marty R. wrote: | | This is representative of the type of puzzle that gives me fits. |
Ditto  |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Tue Jan 22, 2013 10:10 am Post subject: |
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A straightforward solution :
#1. Solving row 2, containing only bivalues : r2c3=6->contradiction :=> r2c3=7; r2c4,r4c3,r3c1=6; r2c7,r9c8=1
#2. NP(89)r8c13 :=> r8c7,r5c9=7
#3. Solving row 5, containing only bivalues : NP(89)r15c2 allows Kite(9R3C2) :=> r5c8=6; singles to the end
Alternatively :
#1. Red Green Transport from r2c3 -> 6r5c8=7r5c9 and 6r5c8=9r5c2=9r3c8 :=> r5c8=6; r5c5=8,r5c2=9,r5c9=7
r2c3=6->r4c4,r5c8=6 [-> ... : contradiction using only singles]
||
r2c3=7->r2c7=1;r8c13=NP(89);r15c2=9;r8c7,r5c9=7;Kite(9R3C2);r5c8=6 [-> ... : solution using only singles]
#2. Pointing : r3c13=9 :=> -9r3c8
#3. XYWing : (7=6)r3c5-(6=17)r2c47 :=> -7r3c8; r3c8=2; singles to the end |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Jan 22, 2013 2:56 pm Post subject: |
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| JC Van Hay wrote: | | A straightforward solution |
Thanks 
| Code: | *--------------------------------------------------------------------*
| 3 789 4 | 1258 578 178 | 1279 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
|----------------------+----------------------+----------------------|
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 679 789 |
| 689 5 3 | 7 4 689 | 289 269 1 |
|----------------------+----------------------+----------------------|
| 2 3789 1 | 589 35678 6789 | 789 4 789 |
| 89 6 789 | 1489 2 14789 | 1789 3 5 |
| 4 3789 5 | 89 378 1789 | 6 179 2 |
*--------------------------------------------------------------------*
(7=89)r1c2,r2c3-(89=7)r238c3 => r2c3=7
*--------------------------------------------------*
| 3 8-9 4 | 12 5 178 | 29 279 6 |
| 5 2 7 | 6 9 3 | 1 8 4 |
| 6 1 a89 | 24 78 478 | 5 b279 3 |
|----------------+----------------+----------------|
| 7 4 6 | 89 1 2 | 3 5 89 |
| 1 d89 2 | 3 68 5 | 4 c69 7 |
| 89 5 3 | 7 4 689 | 289 269 1 |
|----------------+----------------+----------------|
| 2 37 1 | 5 367 67 | 89 4 89 |
| 89 6 89 | 14 2 14 | 7 3 5 |
| 4 37 5 | 89 378 789 | 6 1 2 |
*--------------------------------------------------*
Skyscraper
9r3c3=r3c8-r5c8=9r5c2 => -9r1c2; stte |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jan 22, 2013 6:09 pm Post subject: |
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| arkietech wrote: | | JC Van Hay wrote: | | A straightforward solution |
Thanks
| Code: | *--------------------------------------------------------------------*
| 3 789 4 | 1258 578 178 | 1279 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
|----------------------+----------------------+----------------------|
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 679 789 |
| 689 5 3 | 7 4 689 | 289 269 1 |
|----------------------+----------------------+----------------------|
| 2 3789 1 | 589 35678 6789 | 789 4 789 |
| 89 6 789 | 1489 2 14789 | 1789 3 5 |
| 4 3789 5 | 89 378 1789 | 6 179 2 |
*--------------------------------------------------------------------*
(7=89)r1c2,r2c3-(89=7)r238c3 => r2c3=7
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Dan, in both terms the cell r2c3 (67) is used, but neither ALS term includes a 6.  |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Jan 22, 2013 8:46 pm Post subject: |
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| Marty R. wrote: | | Dan, in both terms the cell r2c3 (67) is used, but neither ALS term includes a 6. |
No, other than infer that if r2c3 had to be a 7 then it could not be a 6.
or if r1c2, r3c3 had to be 89 where would the 7 go?
Maybe there is a better way to show it.  |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Wed Jan 23, 2013 9:34 am Post subject: |
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Dan, if a contradiction is "easy" to prove, it is often more difficult to find a shortest path to it.
Here, a chain of 10 SIS is all that is needed to prove r2c3=6->contradiction.
To wit : r2c3=6->r4c4,r5c8=6;r5c9=7;r5c2=9;r6c6=9;r6c8,r1c7=2;r1c8=9;r2c7=1;no 7 in row 2!
=======================================================================================================
The full explanation is given by writing down vertically the chain in "Eureka Style" (one line per SIS and a "weak link" between 2 SIS being represented on the same "vertical" line).
| Code: | +--------------------+---------------------+-----------------------+
| 3 78(9) 4 | 1258 578 178 | 7(129) 27(19) 6 |
| 5 2 -6(7) | 16 9 3 | (17) 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
+--------------------+---------------------+-----------------------+
| 7 4 8-9(6) | 8(69) 1 2 | 3 5 89 |
| 1 8(9) 2 | 3 8(6) 5 | 4 (679) 8(79) |
| 689 5 3 | 7 4 68(9) | 89(2) (269) 1 |
+--------------------+---------------------+-----------------------+
| 2 3789 1 | 589 35678 6789 | 789 4 789 |
| 89 6 789 | 1489 2 14789 | 1789 3 5 |
| 4 3789 5 | 89 378 1789 | 6 179 2 |
+--------------------+---------------------+-----------------------+
Chain[10] :
6r4c3=6r4c4
6r5c5=6r5c8
7r5c8=7r5c9
9r5c8=9r5c9=9r5c2 ------------------------------------->*
9r4c4===================9r6c6
6r6c8=============9r6c8=2r6c8
2r6c7=2r1c7
9r1c2=============9r1c7=9r1c8
1r1c7=1r1c8=1r2c7
7r2c7=7r2c3 ->**
* : 6r4c3=9r5c2 :=> -9r4c3
** : 6r4c3=7r2c3 :=> -6r2c3 |
Note : the 4 first lines or SIS can be simply written as :
Chain[4] : Wing : 6r4c3=6r4c4-6r5c5=6r5c8-HP(79)79r5c89=9r5c2 :=> -9r4c3
=======================================================================================================
In the alternative path (r5c8=6):
| Code: | +----------------------+---------------------+------------------------+
| 3 78(9) 4 | 1258 578 178 | 1279 1279 6 |
| 5 2 (67) | 16 9 3 | (17) 8 4 |
| 8(69) 1 78(9) | 248 678 4678 | 5 27(9) 3 |
+----------------------+---------------------+------------------------+
| 7 4 89(6) | 89(6) 1 2 | 3 5 89 |
| 1 8(9) 2 | 3 8(6) 5 | 4 -7-9(6) 89(7) |
| 89(6) 5 3 | 7 4 689 | 289 269 1 |
+----------------------+---------------------+------------------------+
| 2 378(9) 1 | 589 35678 6789 | 789 4 89(7) |
| (89) 6 (789) | 1489 2 14789 | (1789) 3 5 |
| 4 378(9) 5 | 89 378 1789 | 6 179 2 |
+----------------------+---------------------+------------------------+
Chain[11] :
6r5c8=6r5c5
6r4c4=6r4c3
6r6c1=6r3c1
6r2c3=======7r2c3
7r2c7=1r2c7
7r8c3=======NP(89)r8c13
1r8c7=89r8c7======7r8c7
7r7c9=7r5c9 ------------------------------->*
9r3c1=============9r79c2==================Kite(9r3c8=9r3c3-9r1c2=9r5c2) ->**
* : 6r5c8=7r5c9 :=> -7r5c8
** : 6r5c8=9r3c8=9r5c2 :=> -9r5c8 |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Wed Jan 23, 2013 6:13 pm Post subject: |
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| Code: | *--------------------------------------------------------------------*
| 3 789 4 | 1258 578 178 | 1279 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
|----------------------+----------------------+----------------------|
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 679 789 |
| 689 5 3 | 7 4 689 | 289 269 1 |
|----------------------+----------------------+----------------------|
| 2 3789 1 | 589 35678 6789 | 789 4 789 |
| 89 6 789 | 1489 2 14789 | 1789 3 5 |
| 4 3789 5 | 89 378 1789 | 6 179 2 |
*--------------------------------------------------------------------* |
1. Finned Squirmbag : 7c25689r13579+7r8c6
Squirmbag =><7>r17c7
Fin =>789r8c136-(789=17)r28c7 -7r17c7
=><7>r17c7
2. 7r7c9-r5c9=(7-6)r5c8=r6c8-r1c8=r4c3-(6=7)r2c3-r2c7=r8c7 : =><7>r7c9
| Code: | *-----------------------------------------------------------*
| 3 789 4 | 128 5 178 | 29 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 89 | 248 678 4678 | 5 279 3 |
|-------------------+-------------------+-------------------|
| 7 4 68 | 69 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 69 7 |
| 689 5 3 | 7 4 689 | 289 269 1 |
|-------------------+-------------------+-------------------|
| 2 37 1 | 5 367 67 | 89 4 89 |
| 89 6 789 | 1489 2 1489 | 17 3 5 |
| 4 3789 5 | 89 37 189 | 6 17 2 |
*-----------------------------------------------------------* |
3. UR37r79c25 : 6r7c5=89r95c2-(89=7)r1c2-(7=6)r2c3-r4c3=r4c4 : =><6>r5c5 sstste |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Thu Jan 24, 2013 11:00 am Post subject: |
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aran: Impressive step 1 !
Could you check your PM after your step 2.
For comparison, here is the one I get :
| Code: | .---------------------.---------------------.---------------------.
| 3 789 4 | 128 5 178 | 29 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
:---------------------+---------------------+---------------------:
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 69 7 |
| 689 5 3 | 7 4 689 | 289 269 1 |
:---------------------+---------------------+---------------------:
| 2 37 1 | 5 367 67 | 89 4 89 |
| 89 6 789 | 1489 2 14789 | 17 3 5 |
| 4 3789 5 | 89 378 1789 | 6 17 2 |
'---------------------'---------------------'---------------------' |
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aran
Joined: 19 Apr 2010
Posts: 70
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| Posted: Fri Jan 25, 2013 5:35 pm Post subject: |
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| JC Van Hay wrote: | aran
Could you check your PM after your step 2.
For comparison, here is the one I get :
| Code: | .---------------------.---------------------.---------------------.
| 3 789 4 | 128 5 178 | 29 1279 6 |
| 5 2 67 | 16 9 3 | 17 8 4 |
| 689 1 789 | 248 678 4678 | 5 279 3 |
:---------------------+---------------------+---------------------:
| 7 4 689 | 689 1 2 | 3 5 89 |
| 1 89 2 | 3 68 5 | 4 69 7 |
| 689 5 3 | 7 4 689 | 289 269 1 |
:---------------------+---------------------+---------------------:
| 2 37 1 | 5 367 67 | 89 4 89 |
| 89 6 789 | 1489 2 14789 | 17 3 5 |
| 4 3789 5 | 89 378 1789 | 6 17 2 |
'---------------------'---------------------'---------------------' |
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J C Van Hay
To determine "knock-on" eliminations, I just hit f11 till Simple Sudoku stops...
For the above, the 7th step of that series of f11 eliminations is an XY-Wing in r5+r4 on 689 leading to <8>r4c4 (as you see available on your grid).
So it would seem that you must cast your net less widely when you calculate these "follow-on" eliminations. |
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