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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Mon Jun 28, 2010 5:03 am Post subject: Puzzle 10/06/28: XY single-stepper |
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| Code: | +-----------------------+
| 6 4 . | . 7 8 | . . . |
| 9 . . | . . 2 | . 7 . |
| . . 7 | 1 9 . | . . . |
|-------+-------+-------|
| . . 8 | . 6 . | . 5 . |
| 3 . 6 | 9 2 . | 1 8 . |
| 4 1 . | . . . | 6 2 . |
|-------+-------+-------|
| . . . | . 1 9 | . . . |
| . 6 . | 8 3 7 | . 1 . |
| . . . | . . . | . . 3 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site
| Code: | after basics
+--------------------------------------------------------------+
| 6 4 123 | 35 7 8 | 259 39 15 |
| 9 35 13 | 356 45 2 | 458 7 1568 |
| 8 235 7 | 1 9 46 | 245 34 56 |
|--------------------+--------------------+--------------------|
| 2 9 8 | 4 6 1 | 3 5 7 |
| 3 7 6 | 9 2 5 | 1 8 4 |
| 4 1 5 | 7 8 3 | 6 2 9 |
|--------------------+--------------------+--------------------|
| 7 23 234 | 26 1 9 | 58 46 58 |
| 5 6 49 | 8 3 7 | 49 1 2 |
| 1 8 29 | 256 45 46 | 7 69 3 |
+--------------------------------------------------------------+
# 39 eliminations remain
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon Jun 28, 2010 10:57 am Post subject: |
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| Quote: | 1)There's an almost<239> XY wing (or chain) in r1c38 and r9c3. The fly in the ointment is the fin, digit 1 in r1c3 - the rest are all bivalues.
So If the fin is true:
(23=1)r1c3-(1=3)r2c3-(3=5)r2c2-(5=4)r2c5-r9c5=(4-6)r9c6=(6-9)r9c8 and r9c8<>9
If fin is false then a simple <239> XY Wing also eliminates the 9 in r9c8
2)Alternatively, there is a blunderbus AIC which creates a discontinuous loop which, (with apologies) I will take all the way round
(9=2)r9c3-(2=13)r12c3-(3=5)r2c2-(5=4)r2c5-r9c5=(4-6)r9c6=(6-9)r9c8=(9)r9c3
If you remove 9 from r9c3 the loop suggests 9 actually belongs in r9c3. (Yes I know we can shorten it.....) |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon Jun 28, 2010 11:50 am Post subject: |
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And finally, | Quote: | viewing the <123> in r12c3 as an ANP, the 2 in r1c3 is all powerful
ANP(13-2)r12c3=r1c7(2-9)=r1c8-r9c8=(9)r9c3 ; r9c3= 9
The converse being
ANP(13=2)r12c3-(2=9)r9c3, r9c3=9 |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Mon Jun 28, 2010 2:44 pm Post subject: |
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Or a wing..!
| Quote: | | m-wing(9) (9=2)r9c3 - r1c3=(2-9)r1c7=r1c8; r9c8<>9 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jun 28, 2010 2:56 pm Post subject: |
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I have not yet found the one step XY solution. However, I have found four different steps that result in the same BUG+1 condition that is needed to complete the puzzle.
I am going to take a break before trying again.
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jun 28, 2010 3:02 pm Post subject: |
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| Mogulmeister wrote: | And finally, | Quote: | viewing the <123> in r12c3 as an ANP, the 2 in r1c3 is all powerful
ANP(13-2)r12c3=r1c7(2-9)=r1c8-r9c8=(9)r9c3 ; r9c3= 9
The converse being
ANP(13=2)r12c3-(2=9)r9c3, r9c3=9 |
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I love it MM 
I have never considered using an AN[PTQ] as pincers to force a common value in a cell, but have always looked for deletions. Nifty idea!
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jun 28, 2010 3:37 pm Post subject: |
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| Mogulmeister wrote: | And finally, | Quote: | viewing the <123> in r12c3 as an ANP, the 2 in r1c3 is all powerful
ANP(13-2)r12c3=(2-9)r1c7=r1c8-r9c8=(9)r9c3 ; r9c3= 9
The converse being
ANP(13=2)r12c3-(2=9)r9c3, r9c3=9 |
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I'm sorry, but I don't see the need for an ANP():
| Code: | (2)r1c3 = (2-9)r1c7 = r1c8 - r9c8 = (9)r9c3 => r9c3<>2
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The <13> pair starting the ANP() contributes nothing to the conclusion. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jun 28, 2010 5:21 pm Post subject: |
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xy-chain.........
| Quote: | | (3=4)r3c8 - (4=6)r7c8 - (6=9)r9c8 - (9=2)r9c3 - (2=3)r7c2; r3c2<>3 |
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jun 28, 2010 5:33 pm Post subject: |
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| daj95376 wrote: | | Mogulmeister wrote: | And finally, | Quote: | viewing the <123> in r12c3 as an ANP, the 2 in r1c3 is all powerful
ANP(13-2)r12c3=(2-9)r1c7=r1c8-r9c8=(9)r9c3 ; r9c3= 9
The converse being
ANP(13=2)r12c3-(2=9)r9c3, r9c3=9 |
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I'm sorry, but I don't see the need for an ANP():
| Code: | (2)r1c3 = (2-9)r1c7 = r1c8 - r9c8 = (9)r9c3 => r9c3<>2
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The <13> pair starting the ANP() contributes nothing to the conclusion. |
Danny, I understand and agree with your comment. However, the only reason that I would ever consider looking at the (2)r1c3 is because of the ANP(13=2)r12c3. While pursuing the ANP, it would be a simple additional task to consider the implication of the (2).
It is interesting that this solution offered by MM is an overlay on the m-wing posted by Peter.
Ted |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jun 28, 2010 8:05 pm Post subject: |
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| tlanglet wrote: | xy-chain.........
| Quote: | | (3=4)r3c8 - (4=6)r7c8 - (6=9)r9c8 - (9=2)r9c3 - (2=3)r7c2; r3c2<>3 |
Ted |
It could be one link shorter: 23 - 26 - 46 - 34 making the same elimination.
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Mon Jun 28, 2010 9:52 pm Post subject: |
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I was looking at different ways rather than going for the obvious M/W wing.
By looking at implications of ANP/AIC different and entertaining solve paths can be explored/rejected - for example, the AIC I referred to as a blunderbus. There are plenty of examples of puzzles here where an AN(PQT) has been chosen in preference to a shorter path and why not ?
I actually posted three versions of where my mind was going on this puzzle - the first looked at (23=1) and finned xy before the twisting it around to the AIC and ANP (2=31) - three solutions and three different ways of viewing the puzzle. I did start off point 3 saying.."viewing the <123> in r12c3 as an ANP, the 2 in r1c3 is all powerful" to explain what had kicked off the thought process......
Remember, some of us jump on these sans solver and just work with the different patterns we see. I will often reject a standard route (especially if I see it early) and look for something more entertaining (for me). In this case ANP implications. It might just also be useful from a practise standpoint for some of those that look at this. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jun 29, 2010 4:36 am Post subject: |
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| I don't know how to do a one-stepper short of testing the move to see where it takes one. My opening four-cell XY-Chain didn't do it, so I followed it with a flightless XY-Wing (694) with pincer transport and a BUG+1. |
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