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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Dec 29, 2007 9:33 pm Post subject: Many Techniques |
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| Code: | Puzzle: M4967446sh(6)
+-------+-------+-------+
| 2 . . | . 1 . | . . . |
| . . . | 3 . 6 | 9 2 . |
| . 1 . | . . . | 7 . . |
+-------+-------+-------+
| 4 . 6 | 1 . . | . . . |
| . 8 9 | . . . | 1 5 . |
| . . . | . . 7 | 6 . 4 |
+-------+-------+-------+
| . 2 4 | . . . | . 9 . |
| . 3 . | 5 . 8 | . . . |
| . . . | . 4 . | . . 5 |
+-------+-------+-------+ |
This one is not very difficult, but at the end you should find (at least) one of each of these to solve it:
1. A BUG+1
2. A W-wing
3. An M-wing
4. About four XY-wings
5. An extended XY-wing
Keith |
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alanr555
Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39
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| Posted: Mon Dec 31, 2007 2:50 am Post subject: Re: Many Techniques |
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| keith wrote: |
This one is not very difficult, but at the end
you should find (at least) one of each of these to solve it:
1. A BUG+1
2. A W-wing
3. An M-wing
4. About four XY-wings
5. An extended XY-wing
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I started out on this one full of expectation that I would find
some challenges requiring the techniques quoted.
I was disappointed!
There are 26 original cells.
A further 40 are resolvable using the Mandatory Pairs techniques
leaving just 15 to be resolved at the end.
Of those fifteen all but one are bi-value cells.
Clearly the target was to eliminate one candidate from the
only cell with three candidates (r5c4 in this case). Thus it was
relatively ease to spot cells amenable to W-wing treatment.
A W-wing was the only technique needed to achieve this.
r3c4 and r5c6 and linked by 2 in column five.
Removing 4 from r5c4 leaves 4 as sole candidate for r5c6
and the rest follows easily.
Sadly my education on
BUG+1
M-wing
Extended XY-wing
will have to wait
- as will practice on XY-wing which I have yet to use after
recent explanations within this forum.
Recent puzzles have demonstrated the power of the W-wing as
just one application of it in each puzzle has been sufficient to
break the impasse after applying the M/Pairs techniques in
conjunction with late setting of the candidate profiles.
I am reluctant to be the first to post a position grid but will do
so if requested to demonstrate the "crunch" position.
In the very early days SamGJ opined that many solvers use
advanced techniques when simpler ones will suffice. Perhaps
it does behove us to look at whether we are making things
too complicated.
That said, a solution derived by any valid technique is a solution
and deserves recognition as such. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 31, 2007 3:47 am Post subject: |
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Alan,
Maybe I should have said, "you can find all of these, any one of which can solve it". This was intended to be a tutorial.
| Code: | +-------------+-------------+-------------+
| 2 69 7 | 8 1 49 | 5 46 3 |
| 8 4 5 | 3 7 6 | 9 2 1 |
| 69 1 3 | 24 29 5 | 7 46 8 |
+-------------+-------------+-------------+
| 4 7 6 | 1 5 3 | 2 8 9 |
| 3 8 9 |24-6 26@ 24# | 1 5 7 |
| 1 5 2 | 9 8 7 | 6 3 4 |
+-------------+-------------+-------------+
| 5 2 4 | 7 3 1 | 8 9 6 |
| 69 3 1 | 5 69 8 | 4 7 2 |
| 7 69 8 | 26@ 4 29# | 3 1 5 |
+-------------+-------------+-------------+ |
1. BUG+1: R5C4 must be <2>. Which solves the puzzle.
2. You seem to have found a W-wing to solve it. I have marked one above. The cells @ <26> are connected by the strong link # on <2> in C6. You can eliminate <6> from R5C4. Which solves the puzzle.
There is at least one other W-wing which solves the puzzle. Can you find it?
How about an M-wing? Or, an extended XY-wing? Not to mention, at least three XY-wings?
Keith |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Mon Dec 31, 2007 6:47 pm Post subject: Many Techniques |
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Keith,
The concept of "M-wing" is new to me.
Cannot find it on the web.
Would you explain it, or offer a reference.
Thanks
Earl |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Mon Dec 31, 2007 8:52 pm Post subject: Many techniques |
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Keith,
Yes, please show the steps in this puzzle.
I suspectd many other readers would also be enlightened.
Thanks,
Earl |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 31, 2007 9:35 pm Post subject: |
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Earl,
I called this an M-wing because:
1. It is a lot like a W-wing
2. It is the simplest thing you will find with Medusa coloring.
| Code: | +-------------+-------------+-------------+
| 2 69 7 | 8 1 49 | 5 46 3 |
| 8 4 5 | 3 7 6 | 9 2 1 |
| 69 1 3 | 24A 29 5 | 7 46 8 |
+-------------+-------------+-------------+
| 4 7 6 | 1 5 3 | 2 8 9 |
| 3 8 9 |246B 26 24C | 1 5 7 |
| 1 5 2 | 9 8 7 | 6 3 4 |
+-------------+-------------+-------------+
| 5 2 4 | 7 3 1 | 8 9 6 |
| 69 3 1 | 5 69 8 | 4 7 2 |
| 7 69 8 |-26 4 29D | 3 1 5 |
+-------------+-------------+-------------+
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As with a W-wing, you should examine cells that have the same two candidates. For example, A and C, which are <24>. Note that you can connect them with two strong links on <4>, via cell B. You have
24 = 4x = 24
All you can say is that A and C have the same value, either <2>, or <4>.
Now, extend the chain to D, which is a strong link on <2>. There are two possibilities:
1. A is <2>.
2. A is not <2>, C is not <2>, D is <2>.
You can exclude <2> from every cell that sees both A and D. In particular, take out <2> in R9C4.
So, a W-wing is two cells with the same candidates that see a strong link:
WX-X=X-WX
and you can exclude W from any cell that sees both ends.
An M-wing is two cells with the same candidates, connected by strong links on one candidate. If you can append a strong link in the other candidate at either end:
MX=X=MX=M or M=MX=X=MX
you can exclude M from any cell that sees both ends.
Keith
(I think am not explaining this very well. It really is quite simple, if you already understand a W-wing.) |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 31, 2007 10:10 pm Post subject: |
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Earl,
Here are a couple more:
| Code: | +-------------+-------------+-------------+
| 2 69 7 | 8 1 49 | 5 46 3 |
| 8 4 5 | 3 7 6 | 9 2 1 |
| 69 1 3 | -24 29F 5 | 7 46 8 |
+-------------+-------------+-------------+
| 4 7 6 | 1 5 3 | 2 8 9 |
| 3 8 9 | 246 26A -24 | 1 5 7 |
| 1 5 2 | 9 8 7 | 6 3 4 |
+-------------+-------------+-------------+
| 5 2 4 | 7 3 1 | 8 9 6 |
| 69 3 1 | 5 69B 8 | 4 7 2 |
| 7 69 8 | 26C 4 29D | 3 1 5 |
+-------------+-------------+-------------+ |
A and C above have the same value, <2> or <6>. They are linked on <6> via cell B.
There is a strong link on <2> in C and D. You can exclude <2> in R5C6, which sees A and D
There is a strong link on <2> in F and A. You can exclude <2> in R3C4, which sees both F and C.
Keith
(And, yes: A and C are also a W-wing that takes out <6> in R5C4.) |
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