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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Wed Jul 15, 2009 9:14 pm Post subject: Puzzle NR_060 |
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| Code: | +-----------------------+
| . . . | 8 . . | . . . |
| . . 9 | . 4 3 | . 7 . |
| . 3 2 | . 7 . | . . 6 |
|-------+-------+-------|
| 3 . . | 2 . . | 4 . 9 |
| . 9 1 | . . 6 | . . . |
| . 4 . | . 9 8 | 6 . 1 |
|-------+-------+-------|
| . . . | 3 . 1 | 2 . . |
| . 2 . | . . . | . 1 . |
| . . 3 | 7 . 9 | . . 4 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Jul 17, 2009 2:28 pm Post subject: |
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A three step solution involving two interacting URs.
First a xy-wing 48-5 with pivot 48 in r3c8 and pseudo-cell 45 in col1 deletes 5 in r5c9.
At this point we have the following code: | Code: |
*--------------------------------------------------------------------*
| 17 17 45 | 8 6 2 | 39 49 35 |
| 68 568 9 | 1 4 3 | 58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
|----------------------+----------------------+----------------------|
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
|----------------------+----------------------+----------------------|
| 46789 5678 4568 | 3 58 1 | 2 689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 1568 3 | 7 2 9 | 58 68 4 |
*--------------------------------------------------------------------* |
Now we have to interacting URs: a type 1 UR 58 in r78c35 that will delete 58 from r7c3, and a type 3 UR 68 in r47c23. To prevent the UR 68, r7c2=(5,7) or r7c3=(4,5) but by taking the UR 58 first, we can still use the UR 68 but the 5 will have been removed from r7c3.
Again, the type 1 UR 58 deletes 58 from r7c3 resulting in the following code: | Code: |
*--------------------------------------------------------------------*
| 17 17 45 | 8 6 2 | 39 49 35 |
| 68 568 9 | 1 4 3 | 58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
|----------------------+----------------------+----------------------|
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
|----------------------+----------------------+----------------------|
| 46789 5678 46 | 3 58 1 | 2 689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 1568 3 | 7 2 9 | 58 68 4 |
*--------------------------------------------------------------------* |
Now, the type 3 UR68 in r47c23 is handled as follows.
a: (4)r7c3 - (4)r1c3 = (4)r3c1 - (4=8)r3c8
b: (5)r7c2 - (5)r2c2 = (5-8)r2c7 = (8)r3c8
c: (7)r7c2 - (7=5)r7c9 - (5=3)r1c9 - (3=9)r1c7 - (9=4)r1c8 - (4=8)r3c8
Thus all three conditions to prevent he UR68 result in r3c8=8 and complete the puzzle.
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Jul 17, 2009 9:17 pm Post subject: |
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this is using Ted's first grid.
| Code: | .---------------------.---------------------.---------------------.
| 17 #17 45 | 8 6 2 |*-39 *49 *35 |
| 68 *568 9 | 1 4 3 |*58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
:---------------------+---------------------+---------------------:
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
:---------------------+---------------------+---------------------:
| 46789 #5678 4568 | 3 58 1 | 2 #689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 #1568 3 | 7 2 9 | 58 #68 4 |
'---------------------'---------------------'---------------------' |
(9)r1c7 = (9)r1c8 - UR68r79c28[(9)r7c8 = (157)r179c2] - (5)r2c2 = (5)r2c7 - (5=3)r1c9; r1c7 <> 3 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Jul 17, 2009 9:22 pm Post subject: |
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Norm, I was wondering about that interaction, but thought I had seen others make deletions in this manner when two steps interacted. Maybe those other circumstances only happened when both moves were valid before either deletions were made. In this case, the UR 68 deletions are not valid if a 5 is in r7c3.
Their are still many points about Sudoku that I do not fully appreciate.
Thanks for the feedback ..............
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Jul 17, 2009 9:32 pm Post subject: |
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| oops, sorry I deleted my initial post. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Jul 17, 2009 10:50 pm Post subject: |
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| storm_norm wrote: | this is using Ted's first grid.
| Code: | .---------------------.---------------------.---------------------.
| 17 #17 45 | 8 6 2 |*-39 *49 *35 |
| 68 *568 9 | 1 4 3 |*58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
:---------------------+---------------------+---------------------:
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
:---------------------+---------------------+---------------------:
| 46789 #5678 4568 | 3 58 1 | 2 #689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 #1568 3 | 7 2 9 | 58 #68 4 |
'---------------------'---------------------'---------------------' |
(9)r1c7 = (9)r1c8 - UR68r79c28[(9)r7c8 = (157)r179c2] - (5)r2c2 = (5)r2c7 - (5=3)r1c9; r1c7 <> 3 |
???
If [r7c8]<>9, then it's true that [r79c2] act as a single pseudo-cell of <157>, but you need two more cells to complete the triple in [c2] for a UR Type 3. I don't see them.
===== ===== ===== Atypical ... Norm Variant
Either [r7c8]=9 or else [r7c1],[r1c8]=9. However, there's a 2-String Kite in <4> with [r7c1],[r1c8] as endpoints. This forces [r7c8]=9 ... and cracks the puzzle.
===== ===== ===== Multicoloring on Two Values
| Code: | PM from Ted, idea from Norm, contradiction found by daj
+-----------------------------------------------------------------------+
| 17 17 45 | 8 6 2 | 39 49 35 |
| 68 568 9 | 1 4 3 | 58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
|-----------------------+-----------------------+-----------------------|
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
|-----------------------+-----------------------+-----------------------|
| 46789 5678 4568 | 3 58 1 | 2 689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 1568 3 | 7 2 9 | 58 68 4 |
+-----------------------------------------------------------------------+
# 40 eliminations remain
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| Code: | B(lue)/G(reen) coloring on 2-String Kite in <4>
+-----------------------------------+
| . . B4 | . . . | . G4 . |
| . . . | . 4 . | . . . |
| G4 . . | . . . | . 4 . |
|-----------+-----------+-----------|
| . . . | . . . | 4 . . |
| . . . | 4 . . | . . . |
| . 4 . | . . . | . . . |
|-----------+-----------+-----------|
| B4 . 4 | . . . | . . . |
| . . . | . . 4 | . . . |
| . . . | . . . | . . 4 |
+-----------------------------------+
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| Code: | P(ink)/A(mber) coloring on strong links in <9>
+-----------------------------------+
| . . . | . . . | 9 P9 . |
| . . 9 | . . . | . . . |
| . . . | 9 . . | . . . |
|-----------+-----------+-----------|
| . . . | . . . | . . 9 |
| . 9 . | . . . | . . . |
| . . . | . 9 . | . . . |
|-----------+-----------+-----------|
| P9 . . | . . . | . A9 . |
| 9 . . | . . . | 9 . . |
| . . . | . . 9 | . . . |
+-----------------------------------+
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If the Pink cells are true for <9>, then there is a contradiction in <4>. Thus, [r7c8]=9 must follow.
Last edited by daj95376 on Fri Jul 17, 2009 11:54 pm; edited 1 time in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Jul 17, 2009 11:44 pm Post subject: |
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| Quote: | | Either [r7c8]=9 or else [r7c1],[r1c8]=9. However, there's a 2-String Kite in <4> with [r7c1],[r1c8] as endpoints. This forces [r7c8]=9 ... and cracks the puzzle |
this is the chain for that atypical variant
(9)r7c8 = (9-4)r1c8 = (4)r1c3 - (4)r3c1 = (4)r7c1; r7c1 <> 9
my UR inference is wrong... looked good tho. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Jul 18, 2009 12:00 am Post subject: |
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revelation:
ok, I found my error in my post that Danny so nicely pointed out. it wasn't the trips that I saw, it was the hidden pair on {6,8} r24c2 that has the strong inference on the 9 in r7c8.
you say what?
I say like this...
notice in the grid below that because of the UR {6,8} r79c28 that the hidden pair {6,8} r24c2 and the 9 in r7c8 cannot both be false.
| Code: | .---------------------.---------------------.---------------------.
| 17 17 45 | 8 6 2 |*39 *49 *35 |
| 68 *568 9 | 1 4 3 |*58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
:---------------------+---------------------+---------------------:
| 3 *68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
:---------------------+---------------------+---------------------:
| 45678 U5678 4568 | 3 58 1 | 2 U689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 U1568 3 | 7 2 9 | 58 U68 4 |
'---------------------'---------------------'---------------------' |
now we can see that the logic works much better.
(9)r1c7 = (9)r1c8 - UR68r79c28[(9)r7c8 = hp(68)r24c2] - (5)r2c2 = (5)r2c7 - (5=3)r1c9; r1c7 <> 3
lets take away the other candidates to show this more clearly.
and you can see that if the hidden pair 68 in r24c2 is false along with the 9 in r7c8, then the {68} UR has to exist in r79c28 which is a no no.
| Code: | +----------+-------+---------+
| . . . | . . . | . . . |
| . 568 . | . . . | . . . |
| . . . | . . . | . . . |
+----------+-------+---------+
| . 68 . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+-------+---------+
| . 68 . | . . . | . 689 . |
| . . . | . . . | . . . |
| . 68 . | . . . | . 68 . |
+----------+-------+---------+ |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Jul 18, 2009 12:19 am Post subject: |
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| storm_norm wrote: | revelation:
ok, I found my error in my post that Danny so nicely pointed out. it wasn't the trips that I saw, it was the hidden pair on {6,8} r24c2 that has the strong inference on the 9 in r7c8.
you say what?
I say like this...
notice in the grid below that because of the UR {6,8} r79c28 that the hidden pair {6,8} r24c2 and the 9 in r7c8 cannot both be false.
| Code: | .---------------------.---------------------.---------------------.
| 17 17 45 | 8 6 2 |*39 *49 *35 |
| 68 *568 9 | 1 4 3 |*58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
:---------------------+---------------------+---------------------:
| 3 *68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
:---------------------+---------------------+---------------------:
| 45678 U5678 4568 | 3 58 1 | 2 U689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 U1568 3 | 7 2 9 | 58 U68 4 |
'---------------------'---------------------'---------------------' |
now we can see that the logic works much better.
(9)r1c7 = (9)r1c8 - UR68r79c28[(9)r7c8 = hp(68)r24c2] - (5)r2c2 = (5)r2c7 - (5=3)r1c9; r1c7 <> 3
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I'm sorry, but I don't see it. It all boils down to applying your AIC from right-to-left. Once you get to [r2c2]=5, all I see is a <1678> Naked Quad remaining in [c2] ... and no linkage to a UR pattern. This is what caught me on the first chain you posted.
The problem with forcing [r79c2]=68 in [c2] is the <68> in [r4c2]. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Jul 18, 2009 12:55 am Post subject: |
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Stealing from Ted's basic theme.
| Code: | Ted's first PM
+-----------------------------------------------------------------------+
| 17 17 45 | 8 6 2 | 39 49 35 |
| 68 568 9 | 1 4 3 | 58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
|-----------------------+-----------------------+-----------------------|
| 3 68 68 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
|-----------------------+-----------------------+-----------------------|
| 46789 68+57 68+45 | 3 58 1 | 2 689 57 |
| 79 2 58 | 6 58 4 | 39 1 37 |
| 168 1568 3 | 7 2 9 | 58 68 4 |
+-----------------------------------------------------------------------+
a) [r7c 3]=4 [r1c3]=5 => [r8c3]<>5
b) [r7c23]=5 => [r8c3]<>5
c) [r7c2 ]=7 [r7c9]=5 [r7c5]<>5 [r8c5]=5 => [r8c3]<>5
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| Code: | reduces to
*-----------------------------------------------------------*
| 17 17 45 | 8 6 2 | 39 49 35 |
| 68 56 9 | 1 4 3 | 58 7 2 |
| 48 3 2 | 9 7 5 | 1 48 6 |
|-------------------+-------------------+-------------------|
| 3 8 6 | 2 1 7 | 4 5 9 |
| 5 9 1 | 4 3 6 | 7 2 8 |
| 2 4 7 | 5 9 8 | 6 3 1 |
|-------------------+-------------------+-------------------|
| 4679 567 45 | 3 8 1 | 2 69 57 |
| 79 2 8 | 6 5 4 | 39 1 37 |
| 16 156 3 | 7 2 9 | 58 68 4 |
*-----------------------------------------------------------*
a) [r7c3]=5 forms {5-8-5-8} DP => [r7c3]<>5
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Puzzle cracks. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Jul 18, 2009 4:02 am Post subject: |
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| Quote: | I'm sorry, but I don't see it. It all boils down to applying your AIC from right-to-left. Once you get to [r2c2]=5, all I see is a <1678> Naked Quad remaining in [c2] ... and no linkage to a UR pattern. This is what caught me on the first chain you posted.
The problem with forcing [r79c2]=68 in [c2] is the <68> in [r4c2]. |
yeah, I might be thinking about this the wrong way, I got a response from ttt over on the players board that he doesn't see it either. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Jul 18, 2009 2:53 pm Post subject: |
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Danny, I love your solution in determining that r8c3<>5 
I tried numerous variations because I was concerned about my posted approach, but just did not find a way to deal with the 5 in r7c3. By ending all the implications in box7, you got around that problem.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Jul 18, 2009 3:43 pm Post subject: |
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| tlanglet wrote: | Danny, I love your solution in determining that r8c3<>5
I tried numerous variations because I was concerned about my posted approach, but just did not find a way to deal with the 5 in r7c3. By ending all the implications in box7, you got around that problem.
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Thanks Ted!
So few people still use this approach because it uses a network based on the UR constraint. If it can't be embedded in a chain, then they ignore it.
BTW: Without your effort, I would have missed it completely. My solver doesn't address this approach, and I seldom tackle them manually. It was fun digging in and working out the details.
Regards, Danny |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jul 21, 2009 5:13 am Post subject: |
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| Couple of XYs, one with transport, couple of Ws, one with transport. |
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