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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Fri Mar 27, 2009 2:58 pm Post subject: Set XY_01 Puzzle 10 |
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| Code: | +-----------------------+
| 9 8 . | . 5 . | . 2 . |
| 6 3 5 | 9 . . | . 8 . |
| . 4 7 | . . . | . 9 . |
|-------+-------+-------|
| . 2 . | . . 6 | . . . |
| 5 . . | . 4 . | . 6 . |
| . . . | 1 . 7 | . . . |
|-------+-------+-------|
| . . . | . . . | 4 . . |
| 4 7 8 | . 9 . | . 5 3 |
| . . . | . . . | . 7 9 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri Mar 27, 2009 6:19 pm Post subject: |
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This one is tough yet looks easy.
I used a UR, skyscraper, and W-wing to get to an easy looking markup. Hah!
I finally found a stretched W-wing that worked enough to get me to a BUG.
Whew! |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Fri Mar 27, 2009 9:45 pm Post subject: |
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I don't like to use UR.
I could not find a "normal" xy-chain.
I found
(7)r2c7 = ((7=2)r5c7 = (2=6)r8c7) - (26=8)r9c7 - (28=6)r9c5 = (6=1)r3c5 = (1=7)r2c5
since r2 cannot have 2 7s, r2c7<>7. This solves the puzzle.
I tried in vain to turn that into a xy-chain to eliminate 7 from r2c7 or 1 from r2c5. Because of the 268 interactions at the bottom, the chain only flows in one direction. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Mar 28, 2009 12:42 am Post subject: |
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| gindaani wrote: | I don't like to use UR.
I could not find a "normal" xy-chain.
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If you don't like URs, then this puzzle probably isn't going to (reasonably) reduce to the XY-Chain/BUG+3 that I found to finish it off. In fact, all of the various techniques that I used seem to help get to the final step. Happy Friday! |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Mar 28, 2009 3:06 pm Post subject: |
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I think this is the wildest puzzle I have ever solved, assuming I did not mess up one particular step.
I started with the UR69, then a finned x-wing on digit <2>, <6>, and <8>, and a xyz 268. At this point I was stuck for a long time. I finally notice a conjugate pair on <7> & <8> that shared a common cell and I was then able to form a chain as follows:
| Code: | *-----------------------------------------------------------*
| 9 8 1 | 367 5 4 | 367 2 67 |
| 6 3 5 | 9 d17 2 | e17 8 4 |
| 2 4 7 | 36 16 8 | 135 9 156 |
|-------------------+-------------------+-------------------|
| 7 2 49 | 5 38 6 | 189 34 18 |
| 5 1 3 | a28 4 9 | f27 6 278 |
| 8 6 49 | 1 23 7 | 59 34 25 |
|-------------------+-------------------+-------------------|
| 3 9 26 | b2678 c678 5 | 4 1 268 |
| 4 7 8 | 26 9 1 | 26 5 3 |
| 1 5 26 | 4 268 3 | 268 7 9 |
*-----------------------------------------------------------* |
If a=2, then
b=8 (strong link 8 col4)
c=7 (strong link 7 row7)
d=1,
e=7,
f=2 which is a conflict with the original assumption; r5c4<>2
(I am unsure how to notate this using Eureka but here is an attempt. I would appreciate anyone providing the "proper" form.
(2-8 )a = (8-7)b = (7)c - (7=1)d - (1=7)e - (7=2)f; a<>2
After cleanup, I had the following code with a "possible" BUG+3 condition.
| Code: | *--------------------------------------------------*
| 9 8 1 | 67 5 4 | 3 2 67 |
| 6 3 5 | 9 17 2 | 17 8 4 |
| 2 4 7 | 3 16 8 | 5 9 16 |
|----------------+----------------+----------------|
| 7 2 9 | 5 3 6 | 18 4 18 |
| 5 1 3 | 8 4 9 | 27 6 27 |
| 8 6 4 | 1 2 7 | 9 3 5 |
|----------------+----------------+----------------|
| 3 9 26 | 267 678 5 | 4 1 28 |
| 4 7 8 | 26 9 1 | 26 5 3 |
| 1 5 26 | 4 68 3 | 268 7 9 |
*--------------------------------------------------*
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All houses contain two occurrences of a digit except box89. In box9, setting r9c7=2 prevents the DP. In box8, setting either r7c45=6 satisfies the constraint of two occurrences in the rows and columns but digit <6> occurs four times in the box. Is this a valid BUG condition? If valid, then setting any of the three conditions forces r8c7=6. This results in a valid BUG+1 which solves the puzzle.
Ted   
[Edit daj95376: made Eureka chain readable. It appeared correct to me.] |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sat Mar 28, 2009 3:37 pm Post subject: |
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I got to your position and looked for a BUG3 also. Box 9 was the problem.
I then saw an almost W-wing as follows.
| Code: | *--------------------------------------------------*
| 9 8 1 |*67 5 4 | 3 2 67 |
| 6 3 5 | 9 *17 2 |*17 8 4 |
| 2 4 7 | 3 16 8 | 5 9 16 |
|----------------+----------------+----------------|
| 7 2 9 | 5 3 6 | 18 4 18 |
| 5 1 3 | 8 4 9 |#27 6 27 |
| 8 6 4 | 1 2 7 | 9 3 5 |
|----------------+----------------+----------------|
| 3 9 26 | 267 678 5 | 4 1 28 |
| 4 7 8 | 2-6 9 1 |#26 5 3 |
| 1 5 26 | 4 68 3 | 268 7 9 |
*--------------------------------------------------* |
The two cells marked "#" combine to make the expected "67". |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Mar 28, 2009 4:07 pm Post subject: |
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| tlanglet wrote: | All houses contain two occurrences of a digit except box89. In box9, setting r9c7=2 prevents the DP. In box8, setting either r7c45=6 satisfies the constraint of two occurrences in the rows and columns but digit <6> occurs four times in the box. Is this a valid BUG condition? If valid, then setting any of the three conditions forces r8c7=6. This results in a valid BUG+1 which solves the puzzle.
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Ted: I mistakenly thought this was a BUG+3 as well. 
After reading wapati's comment, I went back and reviewed the grid. For there to be a BUG after removing the critical candidates, we need ...
1) solved cells plus ...
2) bivalue cells plus ...
3) each candidate occurs exactly twice in a house/unit
If we remove the <6>s in [r7c45] and the <2> in [r9c7], we still have three <2>s in [r7] -- which negates rule (3) for the BUG condition. Too bad because the eliminations worked!!!
[Addendum: besides XY-Chain]
| Code: | <26> DP in [band 3]: [r7c4]=7 or [r9c7]=8 must be true
[r7c4]<>7 => [r7c34]=26 => [r7c9]=8 => [r9c8]<>8 => contradiction!
[r7c4]= 7 => Singles
+-----------------------------------------------------+
| 9 8 1 | 67 5 4 | 3 2 67 |
| 6 3 5 | 9 17 2 | 17 8 4 |
| 2 4 7 | 3 16 8 | 5 9 16 |
|-----------------+-----------------+-----------------|
| 7 2 9 | 5 3 6 | 18 4 18 |
| 5 1 3 | 8 4 9 | 27 6 27 |
| 8 6 4 | 1 2 7 | 9 3 5 |
|-----------------+-----------------+-----------------|
| 3 9 *26 | *26+7 678 5 | 4 1 28 |
| 4 7 8 | *26 9 1 | *26 5 3 |
| 1 5 *26 | 4 86 3 | *26+8 7 9 |
+-----------------------------------------------------+
# 22 eliminations remain
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Last edited by daj95376 on Sat Mar 28, 2009 7:16 pm; edited 5 times in total |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Mar 28, 2009 5:40 pm Post subject: |
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Great move Danny 
Ted |
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