| View previous topic :: View next topic |
| Author |
Message |
cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
|
 Posted: Mon Oct 25, 2010 2:37 pm Post subject: Another Ultra Hard |
 |
|
This is another one of those 6 star Sudoku's that have started appearing in my newspaper. Can't finish it - but then my arsenal is limited to x, xy, xyz wings; URs, ER,s and colouring.
| Code: |
+-------+-------+-------+
| 2 . 9 | 8 . . | . 3 . |
| 7 1 . | . . . | . . . |
| 6 . . | . 9 1 | . . . |
+-------+-------+-------+
| . . . | . 5 4 | . . 9 |
| . 7 . | . . . | . 2 . |
| 8 . . | 9 2 . | . . . |
+-------+-------+-------+
| . . . | 6 1 . | . . 8 |
| . . . | . . . | . 6 3 |
| . 8 . | . . 5 | 4 . 7 |
+-------+-------+-------+
|
|
|
| Back to top |
|
 |
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Mon Oct 25, 2010 5:05 pm Post subject: |
|
|
Here's where I find myself after basics.
| Code: |
+------------+------------+--------------+
| 2 45 9 | 8 467 67 | 56 3 1 |
| 7 1 3458 | 35 46 2 | 9 48 456 |
| 6 345 3458 | 35 9 1 | 578 478 2 |
+------------+------------+--------------+
| 3 26 12 | 7 5 4 | 68 18 9 |
| 9 7 45 | 1 68 368 | 356 2 456 |
| 8 456 145 | 9 2 36 | 3567 147 456 |
+------------+------------+--------------+
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 789 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+------------+------------+--------------+
|
Play this puzzle online at the Daily Sudoku site
A quick scan didn't turn up anything obvious, but I haven't checked for X-Wings. |
|
| Back to top |
|
|
peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
|
| Posted: Mon Oct 25, 2010 5:32 pm Post subject: |
|
|
There are a couple (at least) of chains that complete it after basics. But I could not find an obvious "named" wing move...
This one breaks it - a rather long xy-chain
| Quote: | (4=5)r1c2 - (5=6)r1c7 - (6=8)r4c7 - (8=1)r4c8 - (1=2)r4c3 - (2=7)r8c3 - (7=8)r8c5 - (8=6)r5c5 - (6=4)r2c5 ; r2c3<>4, r1c5<>4
It's long - but just follow the bivalues from one end to the other |
A lot shorter but perhaps more complicated is this 'wing' like chain
| Quote: | w-wing-like(68) ; (8=4)r2c8-(4=6)r2c5 -(6)r2c9=r1c7 - (6=8)r4c7 ; r3c7<>8, r4c8<>8
The strong link of 6s in box 3 connects together a 68 pair and two cells that form a 68 pair - the result is pincers on 8. |
[Edit] There is an xyz-wing also but it doesn't help AFAICS |
|
| Back to top |
|
|
cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
|
| Posted: Mon Oct 25, 2010 6:50 pm Post subject: |
|
|
My original post here was brilliant at the time - but on reflection is a crock. Unfortunately I can't delete once edited. But note - there still is a 345 xyz wing.
Last edited by cgordon on Mon Oct 25, 2010 9:33 pm; edited 6 times in total |
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Mon Oct 25, 2010 7:00 pm Post subject: |
|
|
| Marty R. wrote: | Here's where I find myself after basics.
| Code: |
+------------+------------+--------------+
| 2 45 9 | 8 467 67 | 56 3 1 |
| 7 1 3458 | 35 46 2 | 9 48 456 |
| 6 345 3458 | 35 9 1 | 578 478 2 |
+------------+------------+--------------+
| 3 26 12 | 7 5 4 | 68 18 9 |
| 9 7 45 | 1 68 368 | 356 2 456 |
| 8 456 145 | 9 2 36 | 3567 147 456 |
+------------+------------+--------------+
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 789 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+------------+------------+--------------+
|
Play this puzzle online at the Daily Sudoku site
A quick scan didn't turn up anything obvious, but I haven't checked for X-Wings. |
The DP on 48 in boxes 13 can be killed by a 7 in r3c8, or 3 or 5 in in r23c3. These force r5c9<>6 and r56c7<>5.
Now there's a Type 3 UR on 45 in boxes 46. R6c3 = 1 or r6c9=6. The 1 forces r4c2=6 and the pincers force r4c7 and r6c2<>6. |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Mon Oct 25, 2010 7:12 pm Post subject: |
|
|
A xy-wing with extended vertex which seems to be a shorter version of Peters first solution.
| Quote: | | xy-wing 45-6 with extended vertex: (6=5)r1c7-(5=4)r1c2-r1c5=r2c5-(4=8)r2c8-(8=1)r4c8-(1=2)r4c3-(2=6)r4c2; r4c7<>6 |
Ted |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Mon Oct 25, 2010 8:17 pm Post subject: |
|
|
| Marty R. wrote: | | Marty R. wrote: | Here's where I find myself after basics.
| Code: |
+------------+------------+--------------+
| 2 45 9 | 8 467 67 | 56 3 1 |
| 7 1 3458 | 35 46 2 | 9 48 456 |
| 6 345 3458 | 35 9 1 | 578 478 2 |
+------------+------------+--------------+
| 3 26 12 | 7 5 4 | 68 18 9 |
| 9 7 45 | 1 68 368 | 356 2 456 |
| 8 456 145 | 9 2 36 | 3567 147 456 |
+------------+------------+--------------+
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 789 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+------------+------------+--------------+
|
Play this puzzle online at the Daily Sudoku site
A quick scan didn't turn up anything obvious, but I haven't checked for X-Wings. |
The DP on 48 in boxes 13 can be killed by a 7 in r3c8, or 3 or 5 in in r23c3. These force r5c9<>6 and r56c7<>5.
Now there's a Type 3 UR on 45 in boxes 46. R6c3 = 1 or r6c9=6. The 1 forces r4c2=6 and the pincers force r4c7 and r6c2<>6. |
Marty, I am unable to duplicate the deletions for your first step. Here is what I am able to determine:
If r23c3=3, then r7c3=7, then r8c3=2, then r4c3=1, then r4c8=8, then r4c7=6;
If r23c3=5, then r1c2<>5, then r1c7=5, then r1c7<>6, then r2c9=6
I am unable to find any implications when r3c8=7.
So at this stage, I do not have any common deletions for all the DP-killers; the steps I used provides the potential for pincers on 6 but I still have r3c8=7 as an unresolved DP-killer.
I would greatly appreciate the solutions paths you found to make r5c9<>6 and r56c7<>5.
Ted |
|
| Back to top |
|
|
daj95376
Joined: 23 Aug 2008
Posts: 3854
|
| Posted: Mon Oct 25, 2010 11:02 pm Post subject: |
|
|
My solver didn't find anything interesting, but I stumbled across ...
| Code: | after basics
<45> UR[(1)r6c3 = (6)r56c9] - (6=8)r4c7 - (8=1)r4c7 => r4c3<>1
+--------------------------------------------------------------+
| 2 45 9 | 8 467 67 | 56 3 1 |
| 7 1 3458 | 35 46 2 | 9 48 456 |
| 6 345 3458 | 35 9 1 | 578 478 2 |
|--------------------+--------------------+--------------------|
| 3 26 2-1 | 7 5 4 | 68 18 9 |
| 9 7 *45 | 1 68 368 | 356 2 *45+6 |
| 8 456 *45+1 | 9 2 36 | 3567 47-1 *45+6 |
|--------------------+--------------------+--------------------|
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 789 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+--------------------------------------------------------------+
# 55 eliminations remain
|
I really need to add UR strong inferences to my solver's chain() routine.
[Edit: After Keith's explanation, I realized that I missed the elimination in r6c7. Thanks for catching it Keith!]
Last edited by daj95376 on Tue Oct 26, 2010 3:03 am; edited 1 time in total |
|
| Back to top |
|
|
Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
|
| Posted: Mon Oct 25, 2010 11:09 pm Post subject: |
|
|
| Quote: | | I am unable to find any implications when r3c8=7. |
That 7 forces a 7 in r6c7, leaving r6c6 as the only 3 in that row. The resulting 68 pair in box 5 kills the 6 in r5c9.
I'd rather not go through what I did to rule out the 5s, especially since they don't matter, as the deletion of the 6 in r5c9 sets up the Type 3 on 45. |
|
| Back to top |
|
|
keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
|
| Posted: Mon Oct 25, 2010 11:48 pm Post subject: |
|
|
Danny,
That is a very nice find! After basics:
| Code: | +----------------+----------------+----------------+
| 2 45 9 | 8 47 67 | 56 3 1 |
| 7 1 358 | 35 46 2 | 9 48 56 |
| 6 345 348 | 35 9 1 | 78 47 2 |
+----------------+----------------+----------------+
| 3 26 -12 | 7 5 4 | 68d 18e 9 |
| 9 7 45 | 1 68 368 | 356 2 456c |
| 8 456 145a | 9 2 36 | 3567 -17 456b |
+----------------+----------------+----------------+
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 89 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+----------------+----------------+----------------+ |
For those who don't do chain notation:
Note the UR 45 in R56C39. Either R6C3 is 1 or one of R56C9 is 6. These three cells form a pseudocell 16. This pseudocell together with 68 18 in R4C78 makes an XY-wing. ae are pincers on 1, making the eliminations shown.
It would be interesting to know what the author of the puzzle thinks the solution path is.
Best wishes,
Keith |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Tue Oct 26, 2010 12:29 am Post subject: |
|
|
| Marty R. wrote: | | Quote: | | I am unable to find any implications when r3c8=7. |
That 7 forces a 7 in r6c7, leaving r6c6 as the only 3 in that row. The resulting 68 pair in box 5 kills the 6 in r5c9.
I'd rather not go through what I did to rule out the 5s, especially since they don't matter, as the deletion of the 6 in r5c9 sets up the Type 3 on 45. |
Very nice sequence Marty 
Sometimes I just get lost in the maze.
Ted |
|
| Back to top |
|
|
tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
|
| Posted: Tue Oct 26, 2010 12:34 am Post subject: |
|
|
| keith wrote: | Danny,
That is a very nice find! After basics:
| Code: | +----------------+----------------+----------------+
| 2 45 9 | 8 47 67 | 56 3 1 |
| 7 1 358 | 35 46 2 | 9 48 56 |
| 6 345 348 | 35 9 1 | 78 47 2 |
+----------------+----------------+----------------+
| 3 26 -12 | 7 5 4 | 68d 18e 9 |
| 9 7 45 | 1 68 368 | 356 2 456c |
| 8 456 145a | 9 2 36 | 3567 -17 456b |
+----------------+----------------+----------------+
| 4 39 37 | 6 1 79 | 2 5 8 |
| 5 29 27 | 4 78 89 | 1 6 3 |
| 1 8 6 | 2 3 5 | 4 9 7 |
+----------------+----------------+----------------+ |
For those who don't do chain notation:
Note the UR 45 in R56C39. Either R6C3 is 1 or one of R56C9 is 6. These three cells form a pseudocell 16. This pseudocell together with 68 18 in R4C78 makes an XY-wing. ae are pincers on 1, making the eliminations shown.
It would be interesting to know what the author of the puzzle thinks the solution path is.
Best wishes,
Keith |
And you found a great use for that AUR keith
Ted |
|
| Back to top |
|
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
