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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Thu Oct 15, 2009 7:33 pm Post subject: Nice Endgame |
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This was interesting - with so few cells to solve, how can the ending be so tough? | Code: | Puzzle: M6421419sh(11)
+-------+-------+-------+
| . . 5 | 4 . . | . 3 8 |
| 7 . . | 6 . 2 | . . . |
| . 6 . | . . . | . . 4 |
+-------+-------+-------+
| . 4 . | . 2 . | . 7 9 |
| . . . | 5 . 7 | . . . |
| 5 2 . | . 8 . | . 4 . |
+-------+-------+-------+
| . . . | . . . | . 6 . |
| 8 . . | 2 . 3 | . . 7 |
| 4 . 9 | . . 5 | 3 . . |
+-------+-------+-------+ |
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Oct 15, 2009 8:52 pm Post subject: |
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An unusual approach is to use my Templates Reduction approach that I mentioned in the Players' Forums.
| Code: | Blue/Green coloring on <9> shows only two possibilities.
Amber/Pink coloring on <6> shows only two possibilities.
<9> can not be Blue because it overlays Amber and Pink cells for <6>.
r1c2,r3c4,r5c1,r6c6 <> 9
+---------------------------------------------------------------+
| 2 B19 5 | 4 7 G19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
| G139 6 13 | B19 5 8 | 7 2 4 |
|---------------------+--------------------+--------------------|
| 36 4 8 | 13 2 16 | 5 7 9 |
| B1369A G139 13 | 5 4 7 | 2 8 36P |
| 5 2 7 | G39 8 B69P | 1 4 36A |
|---------------------+--------------------+--------------------|
| 13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
+---------------------------------------------------------------+
# 21 eliminations remain
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Thu Oct 15, 2009 9:03 pm Post subject: |
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I used a long xy-chain and a bug-1
I know the single step answer lies in Row5 col1 13 or the 13 ur but just couldn't see it. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Oct 15, 2009 9:42 pm Post subject: |
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| Code: | .------------------.------------------.------------------.
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
|*139 6 *13 | 19 5 8 | 7 2 4 |
:------------------+------------------+------------------:
| 36 4 8 | 13 2 16 | 5 7 9 |
|136-9 *139 *13 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39 8 69 | 1 4 36 |
:------------------+------------------+------------------:
|*13 *13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
'------------------'------------------'------------------' |
BUGlite {1,3} r357c123
either the 9 in r5c2 or the 9 in r3c1 has to be true to break up the BUG lite pattern.
eliminates the 9 in r5c1
this pattern cannot be allowed to exist or there could be multiple solutions...
| Code: | +----------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| 13 . 13 | . . . | . . . |
+----------+-------+-------+
| . . . | . . . | . . . |
| . 13 13 | . . . | . . . |
| . . . | . . . | . . . |
+----------+-------+-------+
| 13 13 . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+----------+-------+-------+ |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Oct 15, 2009 10:07 pm Post subject: |
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Norm,
Very nice! I stared at the 13 UR / DP for a long time, and did not see it!
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Oct 15, 2009 10:14 pm Post subject: |
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Keith,
thank you,
as an encore move...
| Code: | .------------------.------------------.------------------.
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
|*139 6 *13 |*19 5 8 | 7 2 4 |
:------------------+------------------+------------------:
|-36 4 8 |#13 2 16 | 5 7 9 |
| 1369 139 #13 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39 8 69 | 1 4 36 |
:------------------+------------------+------------------:
|#13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
'------------------'------------------'------------------' |
consider the 1's in row three marked with a star.
regardless which one is true, a 3 at the "#" signs has to be true.
if one of the "#" sign 3's has to be true this eliminates the 3 at r4c1 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Oct 15, 2009 11:05 pm Post subject: |
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I looked and missed Norm's solution, but found a solution using the either of the two UR13.
The first UR13 is in r57c12: either r5c12=9 or r5c1=6. All three conditions imply r5c3=1.
The second UR13 is in r35c13: either r35c1=9 or r5c1=6. All three conditions again imply r5c3=1.
After either UR a BUG+1 forces r5c1=3 to complete the puzzle.
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Oct 15, 2009 11:11 pm Post subject: |
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| storm_norm wrote: | Keith,
thank you,
as an encore move...
| Code: | .------------------.------------------.------------------.
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
|*139 6 *13 |*19 5 8 | 7 2 4 |
:------------------+------------------+------------------:
|-36 4 8 |#13 2 16 | 5 7 9 |
| 1369 139 #13 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39 8 69 | 1 4 36 |
:------------------+------------------+------------------:
|#13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
'------------------'------------------'------------------' |
consider the 1's in row three marked with a star.
regardless which one is true, a 3 at the "#" signs has to be true.
if one of the "#" sign 3's has to be true this eliminates the 3 at r4c1 |
So Norm, what do you call this new pattern? How about "Triple W-Wing" or "Integrated Double W-Wing"? "Only once in a lifetime" may also be an appropriate name.
In any case it was a great find. 
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Oct 15, 2009 11:25 pm Post subject: |
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any of the 1's in row 3 false results in a w-wing {1,3} and eliminates the 3 in r4c1. that is how the pattern molded together for me anyways.
you just have to be sure that whichever 1 you count as false can also be shown to give the same result when considered to be true.
Last edited by storm_norm on Thu Oct 15, 2009 11:30 pm; edited 1 time in total |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Oct 15, 2009 11:28 pm Post subject: |
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| daj95376 wrote: | An unusual approach is to use my Templates Reduction approach that I mentioned in the Players' Forums.
| Code: | Blue/Green coloring on <9> shows only two possibilities.
Amber/Pink coloring on <6> shows only two possibilities.
<9> can not be Blue because it overlays Amber and Pink cells for <6>.
r1c2,r3c4,r5c1,r6c6 <> 9
+---------------------------------------------------------------+
| 2 B19 5 | 4 7 G19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
| G139 6 13 | B19 5 8 | 7 2 4 |
|---------------------+--------------------+--------------------|
| 36 4 8 | 13 2 16 | 5 7 9 |
| B1369A G139 13 | 5 4 7 | 2 8 36P |
| 5 2 7 | G39 8 B69P | 1 4 36A |
|---------------------+--------------------+--------------------|
| 13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
+---------------------------------------------------------------+
# 21 eliminations remain
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Danny, I am not aware of this technique you call Templates Reduction. I follow your logic and it is
A link to your post on the Players Forum would be useful. Also, I am not clear what is meant by the comment "Blue/Green coloring on <9> shows only two possibilities. ".
Ted |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Oct 16, 2009 1:03 am Post subject: |
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Keith's solution:
(Not that it's anything great.)
After basics: | Code: | +----------------+----------------+----------------+
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
| 1-39 6 13@ | 19# 5 8 | 7 2 4 |
+----------------+----------------+----------------+
| 36% 4 8 | 13% 2 16 | 5 7 9 |
| 1369 139 13 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39@ 8 69 | 1 4 36 |
+----------------+----------------+----------------+
| 13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
+----------------+----------------+----------------+ |
The flightless XY-wing 1-39 with pincers @ and with coloring %, takes out <3> in R3C1: | Code: | +-------------+-------------+-------------+
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
| 19# 6 3 | 19# 5 8 | 7 2 4 |
+-------------+-------------+-------------+
|-36 4 8 | 13@ 2 16 | 5 7 9 |
| 369 39 1 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39 8 69 | 1 4 36 |
+-------------+-------------+-------------+
| 13@ 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
+-------------+-------------+-------------+ |
Ignoring the BUG+1, 13@ are a W-wing taking out <3> in R4C1.
Done. Makes my day!
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Oct 16, 2009 3:11 am Post subject: |
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| tlanglet wrote: | Danny, I am not aware of this technique you call Templates Reduction. I follow your logic and it is
A link to your post on the Players Forum would be useful. Also, I am not clear what is meant by the comment "Blue/Green coloring on <9> shows only two possibilities. ".
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Hello Ted,
FWIW: It's nice to have an ISP connection again. Hopefully the tech can get it to be more stable. Working out of the city library sucked!
I debated including an external link on this approach, but then decided that just presenting an example was the way to go.
In my original presentation, I didn't call it anything because it was just an observation based on manipulating Templates in a way that I hadn't done previously. Unfortunately, it didn't seem to be practical for manual solvers. Then I realized that it would work for manual solvers in a very limited scenario.
Templates allow a (computer) solver to determine how many different ways the remaining candidates for a value can be arranged without creating a conflict for that value. When there are only two possible arrangements, all of the candidates for a value can be colored using two colors.
If you have two values whose (respective) candidates can be colored using two colors, then you can easily check for a conflict between selecting one color for the first value and the two colors for the second value. I nicknamed this approach Templates Reduction because of how it works in a computer solver. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Oct 22, 2009 5:22 pm Post subject: |
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| tlanglet wrote: | | storm_norm wrote: | Keith,
thank you,
as an encore move...
| Code: | .------------------.------------------.------------------.
| 2 19 5 | 4 7 19 | 6 3 8 |
| 7 8 4 | 6 3 2 | 9 5 1 |
|*139 6 *13 |*19 5 8 | 7 2 4 |
:------------------+------------------+------------------:
|-36 4 8 |#13 2 16 | 5 7 9 |
| 1369 139 #13 | 5 4 7 | 2 8 36 |
| 5 2 7 | 39 8 69 | 1 4 36 |
:------------------+------------------+------------------:
|#13 13 2 | 7 9 4 | 8 6 5 |
| 8 5 6 | 2 1 3 | 4 9 7 |
| 4 7 9 | 8 6 5 | 3 1 2 |
'------------------'------------------'------------------' |
consider the 1's in row three marked with a star.
regardless which one is true, a 3 at the "#" signs has to be true.
if one of the "#" sign 3's has to be true this eliminates the 3 at r4c1 |
So Norm, what do you call this new pattern? How about "Triple W-Wing" or "Integrated Double W-Wing"? "Only once in a lifetime" may also be an appropriate name.
In any case it was a great find.
Ted |
this is probably the simplest and easy to see "finned w-wing" |
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