| View previous topic :: View next topic |
| Author |
Message |
George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
|
 Posted: Sat Jan 10, 2009 10:49 am Post subject: Can this simple forcing chain be "formalised"? |
 |
|
Given that today's forcing chains often become tomorrow's standard technique, I have a simple focing chain here that I cannot formalise into a conventional logical technique. Can anyone help?
| Code: |
+------------+--------------------+---------------+
| 7 28 1 | 2689 24689 24689 | 3 2459 2459 |
| 5 238 4 | 123789 1289 23789 | 6 129 129 |
| 9 23 6 | 123 5 234 | 7 8 124 |
+------------+--------------------+---------------+
| 34 9 57 | 2578 28 1 | 58 6 23457 |
| 8 147 2 | 567 3 567 | 9 1457 1457 |
| 13 6 57 | 4 289 25789 | 58 1257 12357 |
+------------+--------------------+---------------+
| 146 5 9 | 16 7 46 | 2 3 8 |
| 126 127 8 | 123569 1269 23569 | 4 579 579 |
| 24 247 3 | 2589 2489 24589 | 1 579 6 |
+------------+--------------------+---------------+
|
Play this puzzle online at the Daily Sudoku site
The chain is one that shows that 4 cannot be at r1c5 and so r9c5 must be 4
if r1c5 =4 then r3c4=1, r7c4=6 But also r8c5 =6 so fails
I Know the grid above can be simplified eg 56 in box 5 - but this does not affect the argument! |
|
| Back to top |
|
 |
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Sat Jan 10, 2009 12:01 pm Post subject: |
|
|
| Code: | (4)r1c5 - (4)r3c6 = (4-1)r3c9 = (1)r3c4 - (1=6)r7c4 - (6)r8c5 = (6)r1c5 => [r1c5]<>4
|
Your chain appears to be very generic in nature. I doubt if it has a name. |
|
| Back to top |
|
|
Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
|
| Posted: Sun Jan 11, 2009 11:41 am Post subject: |
|
|
I suspect that George probably saw the chain more in this manner, with the {23} locked set explicit:
(4)r1c5 - ALS[(4)r3c6={23}r3c26] - ({23}=1)r3c4 - (1=6)r7c4 - (6)r8c5=(6-4)r1c5; r1c5<>4
Viewed as such, it still has no name. However, there's another way to see this that can be named. First, note the {1234} ALS in r3c246. This contains the strong inference ALS[(1)r3c4=(4)r3c6], which is a 14 "pseudocell". This can be used to form an "XY-Wing" with <6> pincers:
(6=1)r7c4 - ALSr3c246[(1)r3c4=(4)r3c6] - (4=6)r7c6; r8c5<6> r1c5=6 (i.e. r1c5<>4)
What's more, this "XY-Wing with pseudocell" could be formed with <1> pincers or <4> pincers as well. That's because it's a continuous loop. So we could call it an "XY-Wing with pseudocell loop"! Here it is with a fully reduced basic grid:
| Code: | +---------------+-------------------------+----------------+
| 7 28 1 | 2689 24689 #2689-4 | 3 2459 2459 |
| 5 238 4 |#23789-1 1289 23789 | 6 129 129 |
| 9 23 6 |b123 5 b234 | 7 8 124 |
+---------------+-------------------------+----------------+
| 34 9 57 | 278 28 1 | 58 6 34 |
| 8 14 2 | 56 3 56 | 9 147 147 |
| 13 6 57 | 4 89 789 | 58 12 123 |
+---------------+-------------------------+----------------+
|#14-6 5 9 |a16 7 c46 | 2 3 8 |
| 126 17 8 |#2359-16 #129-6 #2359-6 | 4 579 579 |
| 24 47 3 | 2589 2489 #2589-4 | 1 579 6 |
+---------------+-------------------------+----------------+ |
(6=1)r7c4 - ALSr3c246[(1)r3c4=(4)r3c6] - (4=6)r7c6 - Loop; r2c3<>1; r19c6<>4; r7c1|r8c456<>6
I have marked all those victims with "#".
This grid is actually quite interesting. There is also a Sue de Coq, marked "@" below:
| Code: | +---------------+-------------------------+----------------+
| 7 28 1 | 2689 #46-289 24689 | 3 2459 2459 |
| 5 238 4 | 123789 #1-289 23789 | 6 129 129 |
| 9 23 6 | 123 5 234 | 7 8 124 |
+---------------+-------------------------+----------------+
| 34 9 57 | 278 @28 1 | 58 6 34 |
| 8 14 2 | 56 3 56 | 9 147 147 |
| 13 6 57 | 4 @89 789 | 58 12 123 |
+---------------+-------------------------+----------------+
| 146 5 9 |@16 7 @46 | 2 3 8 |
| 126 17 8 |#2359-16 @1269 #2359-6 | 4 579 579 |
| 24 47 3 | 2589 @2489 #2589-4 | 1 579 6 |
+---------------+-------------------------+----------------+ |
While not what George saw, it has the same overall effect. |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB © 2001, 2005 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
