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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Mon Feb 20, 2012 6:46 pm Post subject: Vanhegan 12 Jul 2011 Fiendish 2.2.1.1 |
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The last move on this one has me stumped.
| Code: |
+-------+-------+-------+
| 4 . 7 | . 5 1 | . . 2 |
| . . . | 3 8 . | . . . |
| . . . | 2 . 6 | . . 1 |
+-------+-------+-------+
| 1 . 6 | . . . | 2 9 . |
| 7 5 . | . . . | . 1 3 |
| . 3 2 | . . . | 6 . 7 |
+-------+-------+-------+
| 6 . . | 1 . 8 | . . . |
| . . . | . 6 5 | . . . |
| 5 . . | 7 9 . | 1 . 4 |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site
Keith
Last edited by keith on Mon Feb 20, 2012 10:32 pm; edited 1 time in total |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Mon Feb 20, 2012 9:35 pm Post subject: |
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#1. M Wing : (8=3)r9c3-3r8c1=(3-8)r3c1=8r6c1 => -8r5c3; 15 Singles
#2. ALS-XY Wing : (982)r39c2-(2374)r249c6-(49)r2c7 => -9r2c12.r3c7; stte
or
#2. 5-SIS AIC : 5r2c3=(5-7)r2c8=7r2c6-(7=3)r4c6-3r9c6=3r9c3-(3=1)r8c3 => -1r2c3; stte |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Feb 21, 2012 12:09 am Post subject: |
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| I used three XY-Wings and an XY-Chain. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Feb 21, 2012 5:12 am Post subject: |
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This puzzle has the strangest ending that I've encountered in quite awhile.
| Code: | after basics and 2x XY-Wing
+-----------------------------------------------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2 19 15 | 3 8 47 | 49 57 6 |
| 39 89 358 | 2 47 6 | 49 57 1 |
|-----------------+-----------------+-----------------|
| 1 4 6 | 8 37 37 | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
|-----------------+-----------------+-----------------|
| 6 7 4 | 1 23 8 | 5 23 9 |
| 39 129 13 | 4 6 5 | 7 23 8 |
| 5 28 38 | 7 9 23 | 1 6 4 |
+-----------------------------------------------------+
# 26 eliminations remain
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Consider r38c1=39. Either r3c1=3 and r8c1=9, or else r3c1=9 and r8c1=3.
If r3c1=3 and r8c1=9, then we've created a BUG !!!
| Code: | +-----------------------------------------------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2 19 15 | 3 8 47 | 49 57 6 |
| 3 89 58 | 2 47 6 | 49 57 1 |
|-----------------+-----------------+-----------------|
| 1 4 6 | 8 37 37 | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
|-----------------+-----------------+-----------------|
| 6 7 4 | 1 23 8 | 5 23 9 |
| 9 12 13 | 4 6 5 | 7 23 8 |
| 5 28 38 | 7 9 23 | 1 6 4 |
+-----------------------------------------------------+
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This leaves r3c1=9 and r8c1=3 to crack the puzzle. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Feb 21, 2012 6:27 am Post subject: |
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| daj95376 wrote: | This puzzle has the strangest ending that I've encountered in quite awhile.
| Code: | after basics and 2x XY-Wing
+-----------------------------------------------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2 19 15 | 3 8 47 | 49 57 6 |
| 39 89 358 | 2 47 6 | 49 57 1 |
|-----------------+-----------------+-----------------|
| 1 4 6 | 8 37 37 | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
|-----------------+-----------------+-----------------|
| 6 7 4 | 1 23 8 | 5 23 9 |
| 39 129 13 | 4 6 5 | 7 23 8 |
| 5 28 38 | 7 9 23 | 1 6 4 |
+-----------------------------------------------------+
# 26 eliminations remain
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Consider r38c1=39. Either r3c1=3 and r8c1=9, or else r3c1=9 and r8c1=3.
If r3c1=3 and r8c1=9, then we've created a BUG !!!
| Code: | +-----------------------------------------------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2 19 15 | 3 8 47 | 49 57 6 |
| 3 89 58 | 2 47 6 | 49 57 1 |
|-----------------+-----------------+-----------------|
| 1 4 6 | 8 37 37 | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
|-----------------+-----------------+-----------------|
| 6 7 4 | 1 23 8 | 5 23 9 |
| 9 12 13 | 4 6 5 | 7 23 8 |
| 5 28 38 | 7 9 23 | 1 6 4 |
+-----------------------------------------------------+
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This leaves r3c1=9 and r8c1=3 to crack the puzzle. |
Two XY-wings get me here: | Code: | +-------------+-------------+-------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2 19 15 | 3 8 47 | 49 57 6 |
| 39 89 358 | 2 47 6 | 49 57 1 |
+-------------+-------------+-------------+
| 1 4 6 | 8 37 37 | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
+-------------+-------------+-------------+
| 6 7 4 | 1 23 8 | 5 23 9 |
| 39 129 13 | 4 6 5 | 7 23 8 |
| 5 28 38 | 7 9 23 | 1 6 4 |
+-------------+-------------+-------------+ |
There are two reasons I posted this:
1. This is not a BUG+n.
2. The chains are quite long, and I see no hint of a pattern to give me a clue. (I have yet to look at JC's M-wing.)
Danny, I do not think your logic is correct. Maybe I don't understand, but not a BUG is not a BUG. Making an elimination to create a BUG is not valid.
Best wishes,
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Feb 21, 2012 6:36 am Post subject: |
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| JC Van Hay wrote: | #1. M Wing : (8=3)r9c3-3r8c1=(3-8)r3c1=8r6c1 => -8r5c3; 15 Singles
#2. ALS-XY Wing : (982)r39c2-(2374)r249c6-(49)r2c7 => -9r2c12.r3c7; stte
or
#2. 5-SIS AIC : 5r2c3=(5-7)r2c8=7r2c6-(7=3)r4c6-3r9c6=3r9c3-(3=1)r8c3 => -1r2c3; stte |
JC, to which grid does your M-wing apply? In my grid, posted in the last message, I see no hope of a wing.
Keith |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Tue Feb 21, 2012 8:05 am Post subject: |
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| keith wrote: | | JC Van Hay wrote: | #1. M Wing : (8=3)r9c3-3r8c1=(3-8)r3c1=8r6c1 => -8r5c3; 15 Singles
#2. ALS-XY Wing : (982)r39c2-(2374)r249c6-(49)r2c7 => -9r2c12.r3c7; stte
or
#2. 5-SIS AIC : 5r2c3=(5-7)r2c8=7r2c6-(7=3)r4c6-3r9c6=3r9c3-(3=1)r8c3 => -1r2c3; stte |
JC, to which grid does your M-wing apply? In my grid, posted in the last message, I see no hope of a wing.
Keith |
Here is a copy of my notes containing the corresponding grids.
| Code: | #1. M Wing :
+-------------------+-------------+----------------+
| 4 6 7 | 9 5 1 | 38 38 2 |
| 29 129 159 | 3 8 47 | 4579 457 6 |
| 9(38) 89 3589 | 2 47 6 | 4579 457 1 |
+-------------------+-------------+----------------+
| 1 4 6 | 58 37 37 | 2 9 58 |
| 7 5 9-8 | 6 24 249 | 48 1 3 |
| 9(8) 3 2 | 58 1 49 | 6 458 7 |
+-------------------+-------------+----------------+
| 6 279 4 | 1 23 8 | 357 2357 59 |
| 29(3) 1279 139 | 4 6 5 | 378 2378 89 |
| 5 28 (38) | 7 9 23 | 1 6 4 |
+-------------------+-------------+----------------+
(8=3)r9c3-3r8c1=(3-8)r3c1=8r6c1 => -8r5c3; 15 Singles
#2. 5-SIS AIC :
+-----------------+-------------+-------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 29 129 -1(5) | 3 8 4(7) | 49 (57) 6 |
| 39 89 358 | 2 47 6 | 49 57 1 |
+-----------------+-------------+-------------+
| 1 4 6 | 8 37 (37) | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
+-----------------+-------------+-------------+
| 6 7 4 | 1 23 8 | 5 23 9 |
| 239 129 (13) | 4 6 5 | 7 23 8 |
| 5 28 8(3) | 7 9 2(3) | 1 6 4 |
+-----------------+-------------+-------------+
5r2c3=(5-7)r2c8=7r2c6-(7=3)r4c6-3r9c6=3r9c3-(3=1)r8c3 => -1r2c3; stte
or
#2. 6-SIS ALS-XY Wing :
+----------------+-------------+-------------+
| 4 6 7 | 9 5 1 | 3 8 2 |
| 2-9 12-9 15 | 3 8 (47) | (49) 57 6 |
| 39 (89) 358 | 2 47 6 | 4-9 57 1 |
+----------------+-------------+-------------+
| 1 4 6 | 8 37 (37) | 2 9 5 |
| 7 5 9 | 6 24 24 | 8 1 3 |
| 8 3 2 | 5 1 9 | 6 4 7 |
+----------------+-------------+-------------+
| 6 7 4 | 1 23 8 | 5 23 9 |
| 239 129 13 | 4 6 5 | 7 23 8 |
| 5 (28) 38 | 7 9 (23) | 1 6 4 |
+----------------+-------------+-------------+
(982)r39c2-(2374)r249c6-(49)r2c7 => -9r2c12.r3c7; stte |
BTW, Danny's logic is correct : no BUG+2 doesn't prevent the use of a BUG in a line of reasoning as Danny did.
Best regards, JC. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Feb 21, 2012 9:03 am Post subject: |
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| keith wrote: | There are two reasons I posted this:
1. This is not a BUG+n.
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I don't consider it a BUG+n. That's why I didn't present it as such. However, I would be surprised if RonK doesn't have an advanced definition of BUG+n in which it would qualify.
| you wrote: | 2. The chains are quite long, and I see no hint of a pattern to give me a clue. (I have yet to look at JC's M-wing.)
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I'm not sure how/why you are using chains. After assigning r3c1=3 and r8c1=9, I used Simple Sudoku to examine the candidates for each value -- except <6>. For every value, the candidates appeared twice in every row/column/box that they occupied. To me, this is a fundamental property of a BUG.
| you wrote: | Danny, I do not think your logic is correct. Maybe I don't understand, but not a BUG is not a BUG. Making an elimination to create a BUG is not valid.
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I disagree. The whole concept of a BUG+n is based on the assumption of one or more eliminations. Consider this BUG+1.
| Code: | +-----------------------+
| 2 . . | . . . | . . 9 |
| . . 8 | . . . | 7 . . |
| . 1 . | 6 8 7 | . 2 . |
|-------+-------+-------|
| . . . | 5 . . | 8 . . |
| . . 7 | . 1 . | 9 . . |
| . . 5 | . . 4 | . . . |
|-------+-------+-------|
| . 4 . | 8 2 5 | . 9 . |
| . . 6 | . . . | 4 . . |
| 9 . . | . . . | . . 7 |
+-----------------------+
*--------------------------------------------------*
| 2 7 4 | 13 5 13 | 6 8 9 |
| 6 5 8 | 49 49 2 | 7 3 1 |
| 3 1 9 | 6 8 7 | 5 2 4 |
|----------------+----------------+----------------|
| 1 69 2 | 5 7 69 | 8 4 3 |
| 4 3 7 | 2 1 8 | 9 6 5 |
| 8 69 5 | 39 36+9 4 | 1 7 2 |
|----------------+----------------+----------------|
| 7 4 1 | 8 2 5 | 3 9 6 |
| 5 2 6 | 7 39 39 | 4 1 8 |
| 9 8 3 | 14 46 16 | 2 5 7 |
*--------------------------------------------------*
BUG+1 = 9 r6c5
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The logic goes: If <9> is eliminated from r6c5, then a BUG results. So, r6c5=9 must follow.
What makes my solution different is that I use two assignments to create a BUG. Since those assignments can't be valid, the complementary assignments must be valid.
An alternate way of viewing my logic:
| Code: | r3c3<>3 r3c1=3 r8c1=9 r8c2<>9; BUG => r3c3=3
-or-
r8c2<>9 r8c1=9 r3c1=3 r3c3<>3; BUG => r8c2=9
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Regards, Danny |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Feb 21, 2012 6:05 pm Post subject: |
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| Quote: | 1. This is not a BUG+n.
2. The chains are quite long, and I see no hint of a pattern to give me a clue. (I have yet to look at JC's M-wing.)
Danny, I do not think your logic is correct. Maybe I don't understand, but not a BUG is not a BUG. Making an elimination to create a BUG is not valid. |
Keith, I don't understand your reasoning. Agree it's not a BUG+, but what's not valid? He's ruling out something that leads to an invalidity (the BUG). An argument can be made that there's a trial-and-error element, but what's not correct or not valid? |
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Clement
Joined: 24 Apr 2006
Posts: 1113
Location: Dar es Salaam Tanzania
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| Posted: Tue Feb 21, 2012 6:46 pm Post subject: Vanhegan 12 Jul 2011 Fiendish2.2.1.1 |
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| I agree with keith that ''making an elimination to create a BUG is not valid''. In BUG+2 the extra candidates in the two 3 candidate cells do not necessarily have to be solutions in both cells. In this puzzle it is just a coincidence that they are solutions to both cells. What you have to do is to consider the consequences of the extra candidates being solutions in those cells to other cells. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Feb 21, 2012 9:27 pm Post subject: Re: Vanhegan 12 Jul 2011 Fiendish2.2.1.1 |
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| Clement wrote: | | I agree with keith that ''making an elimination to create a BUG is not valid''. In BUG+2 the extra candidates in the two 3 candidate cells do not necessarily have to be solutions in both cells. In this puzzle it is just a coincidence that they are solutions to both cells. What you have to do is to consider the consequences of the extra candidates being solutions in those cells to other cells. |
A good example of the conflict between truth (logic) and rules (form). |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Feb 22, 2012 2:03 am Post subject: |
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Danny's result and logic are correct, but I think the logic is a little fortuitous.
I've looked long and hard at this, and I cannot find the reverse argument: What are all the conditions to prevent a BUG?
Keith |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Feb 22, 2012 2:37 am Post subject: |
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| daj95376 wrote: | The logic goes: If <9> is eliminated from r6c5, then a BUG results. So, r6c5=9 must follow.
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Truth cannot be fortuitous. It must be true or it is false.
If r6c5 is a not a 9 then the puzzle has multiple answers (no ifs ands or buts). If this is true then r6c5 must be a 9 to have a valid puzzle.
or ami I confused? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Feb 22, 2012 4:11 am Post subject: |
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| arkietech wrote: | | daj95376 wrote: | The logic goes: If <9> is eliminated from r6c5, then a BUG results. So, r6c5=9 must follow.
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Truth cannot be fortuitous. It must be true or it is false.
If r6c5 is a not a 9 then the puzzle has multiple answers (no ifs ands or buts). If this is true then r6c5 must be a 9 to have a valid puzzle.
or ami I confused? |
"Fortuitous" means fortunate. It does not mean correct or incorrect, nor right or wrong.
Sure, R3C1=3 forces a BUG. That is very cool but, I think that is a lucky (fortuitous) observation.
I cannot for the life of me see how not a BUG forces R3C1=9.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Feb 22, 2012 4:47 am Post subject: |
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| Quote: | | Sure, R3C1=3 forces a BUG. That is very cool but, I think that is a lucky (fortuitous) observation. |
Are we into a semantical game here? Why wasn't it a skilled observation?
| Quote: | | I cannot for the life of me see how not a BUG forces R3C1=9. |
What is the significance of that, given that it was discovered that r3c1=3 forces a BUG? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Feb 22, 2012 5:11 am Post subject: |
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| Marty R. wrote: | | Are we into a semantical game here? Why wasn't it a skilled observation? |
Because it's my opinion, and I don't see a method for making that observation.
| Marty R. wrote: | | Quote: | | I cannot for the life of me see how not a BUG forces R3C1=9. |
What is the significance of that, given that it was discovered that r3c1=3 forces a BUG? |
Because I am looking for a method.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Feb 22, 2012 6:10 am Post subject: |
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| keith wrote: | Because I am looking for a method.
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Fortuitous is in the eyes of the beholder. Here's how I became fortuitous!
I was looking for a BUG+2 scenario because there were only two unsolved cells with more than two candidates. So, I started examining the candidates in r3c3 and r8c2 to see if I could find the proper conditions for a BUG+2.
What I discovered was that the <3> in r3c3 occurred three times in [c3] -- which was good -- but only twice in [r3] and [b1] -- which was bad because temporarily performing r3c3<>3 would leave a Hidden Single in the form of r3c1=3.
Similarly, I discovered that the <9> in r8c2 occurred three times in [c2] -- which was good -- but only twice in [r8] and [b7] -- which was bad because temporarily performing r8c2<>9 would leave a Hidden Single in the form of r8c1=9.
Here's where the fortuitous part of the story enters. While I was licking my wounds over the "bad" part of of the conditions above, I noticed that the only unsolved cells in [c1] were the <39> pair. Then's when it hit me that the combination of assignments, r3c1=3 and r8c1=9, might force a BUG to occur. So, I tried it and discovered that my hunch was correct.
Of course, trying to explain it took on a whole life of its own. _  _
If a puzzle has a single/unique solution, then a BUG is just another pattern that can't exist. I discount speculation that it would lead to multiple solutions because there is only one solution present ... MAX. Instead, it will always lead to zero solutions being found.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Feb 22, 2012 6:34 am Post subject: |
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OK Danny,
So how do we solve these BUGgers?
End games that are dominated by bivalue cells but which are not BUG+n patterns are, I think, rare.
Do you have other examples? Maybe there is an Almost-BUG method to be found.
In the current puzzle, I was totally frustrated in trying to take the "could be a BUG" idea to any conclusion.
I hope you understand I am not criticizing your astute observation that Cell Value => BUG.
I am looking for possible situations where BUG => Cell Value.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Feb 22, 2012 6:55 am Post subject: |
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| keith wrote: | OK Danny,
So how do we solve these BUGgers?
End games that are dominated by bivalue cells but which are not BUG+n patterns are, I think, rare.
Do you have other examples? Maybe there is an Almost-BUG method to be found.
In the current puzzle, I was totally frustrated in trying to take the "could be a BUG" idea to any conclusion.
I hope you understand I am not criticizing your astute observation that Cell Value => BUG.
I am looking for possible situations where BUG => Cell Value.
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I don't (currently) have any other examples, but I do know that they may not be as rare as you might expect. Back when I was writing my first Sudoku solver, I forgot to include the test for Hidden Singles in my BUG+1 routine. I encountered several puzzles where the "solution" from my solver was garbage after the BUG+1 routine!
Bottom Line: All of the patterns like UR, BUG, MUG, and such are never suppose to occur in the solution for a puzzle with a single/unique solution. If you can create a scenario where any of these patterns occur, then you've done something wrong. To me, knowing that I could have done something wrong is just as helpful as knowing what's right. _  _ |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Feb 22, 2012 1:44 pm Post subject: |
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great exhange! I am fortuitous to have followed it. 
and that is the truth. |
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