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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sat Jan 30, 2010 1:13 am Post subject: Puzzle 10/01/29 (B) |
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XYZ-Wing alert. (scrapping the bottom of the barrel in this file of puzzles.)
| Code: | +-----------------------+
| 7 . . | . 6 . | . . . |
| . 8 . | . 7 . | 6 5 9 |
| . . . | . . 3 | . . . |
|-------+-------+-------|
| . . . | 5 9 . | 3 . . |
| 5 1 . | 3 . . | 7 . . |
| . . 4 | . . 6 | . 1 . |
|-------+-------+-------|
| . 5 . | 6 3 . | 9 2 . |
| . 3 . | . . 9 | 8 . 1 |
| . 6 . | . . . | . 3 . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jan 30, 2010 5:34 pm Post subject: |
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| Another puzzle where I just played what I saw. There was an XYZ, XY, two multi-colorings and two flightless XYs, both with pincer transports. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Feb 01, 2010 1:19 am Post subject: |
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I saw a x-wing on 8 in r36c58 while performing basics, and had to start with that.
Then, because of the XYZ alert, I started looking for them and found xyz-wing 2-48 in r3c9 that deleted 4 from r3c7.
At that point, I had the following code.
| Code: | *-----------------------------------------------------------*
| 7 24 9 | 18 6 5 | 124 48 3 |
| 1 8 3 | 24 7 24 | 6 5 9 |
| 6 24 5 | 9 18 3 | 12 7 248 |
|-------------------+-------------------+-------------------|
| 28 7 268 | 5 9 1 | 3 48 246 |
| 5 1 268 | 3 24 248 | 7 9 26 |
| 3 9 4 | 7 28 6 | 25 1 258 |
|-------------------+-------------------+-------------------|
| 48 5 1 | 6 3 478 | 9 2 47 |
| 24 3 7 | 24 5 9 | 8 6 1 |
| 9 6 28 | 18 124 2478 | 45 3 457 |
*-----------------------------------------------------------*
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Still looking for xyz-wings, I saw the possible xzy-wing 124 in r1c7.
(1)r1c7 - (1=2)r3c7; r3c9<>2,
(2)r1c7; r3c9<>2,
(4)r1c7 - r1c8 = r4c8 - (4)r4c9 = Subset(26)r45c9; r3c9<>2.
So all three values of cell c1c7 remove 2 from r3c9.
I looked for another xyz-wing but failed. I finished the puzzle with a w-wing 28 and a BUG+1.
Ted  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Feb 01, 2010 2:05 am Post subject: |
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| Quote: | Still looking for xyz-wings, I saw the possible xzy-wing 124 in r1c7.
(1)r1c7 - (1=2)r3c7; r3c9<>2,
(2)r1c7; r3c9<>2,
(4)r1c7 - r1c8 = r4c8 - (4)r4c9 = Subset(26)r45c9; r3c9<>2.
So all three values of cell c1c7 remove 2 from r3c9. |
Ted,
Notwithstanding the 26 subset, you'll have to educate me. If r1c7=4, why isn't r1c8=8 and, therefore, r3c9=2? The 26 subset can be created but that would leave three cells in box 3 that have to be 4 or 8. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Feb 01, 2010 3:56 am Post subject: |
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With the XYZ-Wing alert, I didn't expect this puzzle to cause excessive problems.
| Code: | r2 b2 Locked Pair <> 24 r1c4,r3c5
c4 Naked Pair <> 24 r19c4
r5 b5 Locked Candidate 1 <> 4 r5c9
r36 X-Wing <> 8 r59c5,r45c9
r57c6 Skyscraper <> 8 r4c1,r9c3
<28+4> XYZ-Wing r3c9/r1c8+r3c2 <> 4 r3c7
<18+2> XY-Wing r3c5/r3c7+r6c5 <> 2 r6c7
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Regards, Danny |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Feb 01, 2010 2:08 pm Post subject: |
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| Marty R. wrote: | | Quote: | Still looking for xyz-wings, I saw the possible xzy-wing 124 in r1c7.
(1)r1c7 - (1=2)r3c7; r3c9<>2,
(2)r1c7; r3c9<>2,
(4)r1c7 - r1c8 = r4c8 - (4)r4c9 = Subset(26)r45c9; r3c9<>2.
So all three values of cell c1c7 remove 2 from r3c9. |
Ted,
Notwithstanding the 26 subset, you'll have to educate me. If r1c7=4, why isn't r1c8=8 and, therefore, r3c9=2? The 26 subset can be created but that would leave three cells in box 3 that have to be 4 or 8. |
Marty, here are a couple of comments in response to your question.
First, I think your own observation that the path I presented results in a conflict or invalid condition is important. If we also continue my chain this conclusion is obvious.
(4)r1c7 - r1c8 = r4c8 - (4)r4c9 = Subset(26)r45c9 - (2)r3c9 = Subset(48)r34c9; r1c7<>4 (which is true when the puzzle is solved)
Some time ago I spotted a conflicting situation similar to this and asked for clarification. I was told that any path is valid to make an inference and I have seen conditions in other posts where conflicting conditions existed and the path of interest was used.
Hopefully someone else will be able to help both of us with a good explanation.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Feb 01, 2010 4:02 pm Post subject: |
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In logic, if you start with a true premise, then everything derived from that premise is true. If you start with a false premise, then you have no guarantee about the validity of anything derived. However, that doesn't mean that the results are useless because a false premise may lead to a truth. This is the basis for many Sudoku techniques!
A forcing chain, such as Ted's, is based on the principle that one premise must be true ... and any chain from it is true. All that's then needed is to find chains where all of the false premises produce the same conclusion. Even without knowing which of the original premises is true, you are able to derive a conclusion that's true. Impressive!
Even a Naked Pair is based on a forcing network. No matter which candidate value is assumed true in one bivalue cell, it forces the other candidate to be true in another bivalue cell. The combined result is that neither of those candidate values can be true in any cells that see these two cells. Eliminations result even though you don't know which value is true in the original cells. |
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Mon Feb 01, 2010 4:42 pm Post subject: |
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| tlanglet wrote: | At that point, I had the following code.
| Code: | *-----------------------------------------------------------*
| 7 24 9 | 18 6 5 | 124 48 3 |
| 1 8 3 | 24 7 24 | 6 5 9 |
| 6 24 5 | 9 18 3 | 12 7 248 |
|-------------------+-------------------+-------------------|
| 28 7 268 | 5 9 1 | 3 48 246 |
| 5 1 268 | 3 24 248 | 7 9 26 |
| 3 9 4 | 7 28 6 | 25 1 258 |
|-------------------+-------------------+-------------------|
| 48 5 1 | 6 3 478 | 9 2 47 |
| 24 3 7 | 24 5 9 | 8 6 1 |
| 9 6 28 | 18 124 2478 | 45 3 457 |
*-----------------------------------------------------------*
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Still looking for xyz-wings, I saw the possible xzy-wing 124 in r1c7.
(1)r1c7 - (1=2)r3c7; r3c9<>2,
(2)r1c7; r3c9<>2,
(4)r1c7 - r1c8 = r4c8 - (4)r4c9 = Subset(26)r45c9; r3c9<>2.
So all three values of cell c1c7 remove 2 from r3c9. |
As AIC, I think that we can write your deduction like: (12=4)r13c7-(4)r1c8=(4)r4c8-(4=26)r45c9 => r3c9 & r6c7<>2
ttt |
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