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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Thu Nov 08, 2007 8:10 pm    Post subject: More Interesting ... Reply with quote
This puzzle is more interesting than most I have done this week:
Code:
..92.34..
..6.4.3..
23.7.8.95
6.8...5.1
.7.....6.
1.3...9.7
36.4.7.19
..1.9.7..
..73.16..

It is a random super hard from the Brain Basher site.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Thu Nov 08, 2007 11:13 pm    Post subject: Reply with quote
Quote:
This puzzle is more interesting than most I have done this week:


I don't know what you've done this week, but it is interesting. Wink

I suspect your first move was the same as mine, a UR of a type that isn't that frequent. Thereafter it was an XYZ-Wing, two W-Wings and an ER which finished it off. Since those last two techniques are relatively new to me, I'm not sure what I could've done otherwise, except search for X-Wings and skyscrapers, which, for some reason, I hate doing.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Fri Nov 09, 2007 12:35 am    Post subject: Reply with quote
Marty's suspicions are correct. The shortest route I found is an X-Wing, XY-Wing and Skyscraper. I won't give away where they are, though.

I also found a route with a W-Wing on {24}, a (different) X-Wing, a UR (probably the same as Marty's, but now reduced to the simplest type), then a BUG+1.

Here is something I found interesting:
Code:
+------------+-------------+----------------+
| 578 58  9  | 2  1   3    | 4    78    6   |
| 78  1   6  | 5  4   9    | 3    278  A28  |
| 2   3   4  | 7  6   8    | 1    9     5   |
+------------+-------------+----------------+
| 6   24  8  | 9  7   24   | 5    3     1   |
| 9   7   25 | 1  3   245  | 28   6    A248 |
| 1   245 3  | 68 258 2456 | 9   A24    7   |
+------------+-------------+----------------+
| 3   6   25 | 4  258 7    | 28   1     9   |
| 458 258 1  | 68 9   256  | 7    2458  3   |
| 458 9   7  | 3  258 1    | 6    2458 -248 |
+------------+-------------+----------------+

Note the otherwise useless XYZ Wing marked "A". (I've been on the lookout for these due to the recent posts.) And, note the strongly linked <2>s in Box 3.

If R6C8 is <2>, then R2C9 is <2>. If R6C8 is not <2>, then one of R26C9 is <2>. In either case, R9C9 cannot be <2>.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Nov 09, 2007 3:02 am    Post subject: Coloring the pivot Reply with quote
If you solve this puzzle using a regular hierarchy of methods (from the position posted by Asellus) you will find an X-wing, an XY-wing, a Type 1 UR and a BUG+1.

After the first two of these:
Code:
+-------------+-------------+-------------+
| 578 58  9   | 2   1   3   | 4   78  6   |
| 78  1   6   | 5   4   9   | 3   78  2   |
| 2   3   4   | 7   6   8   | 1   9   5   |
+-------------+-------------+-------------+
| 6   4   8   | 9   7   2   | 5   3   1   |
| 9   7   25A | 1   3   45  | 28  6   48  |
| 1   25a 3   | 68  58c 456 | 9   24  7   |
+-------------+-------------+-------------+
| 3   6   25a | 4   5-8  7   | 28b 1   9   |
| 458 258 1   | 68  9   56  | 7   245 3   |
| 458 9   7   | 3   2   1   | 6   45  48  |
+-------------+-------------+-------------+

Note the three cells a-A-a <25>. Those marked a have the same value. With b and c they form an XY-wing 58-25-28. You can remove <8> from any cell that sees both b and c. In particular, removing <8> from R7C5 solves the puzzle.

Or, the UR on <78> is in R12.

Keith
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Nov 09, 2007 3:29 am    Post subject: Reply with quote
Asellus wrote:
... Here is something I found interesting ...

Yes, quite interesting! Idea

But, I suspect, quite rare. If I may add my own explanation:

An XYZ-wing is a triple that is not in one row, column or box. It is of the form XY-XYZ-XZ. Any cell that sees all three of the XYZ-wing cells cannot be X. The logic is: One of the three cells is X.

Asellus has pointed out a coloring that says if XY is X, then XZ is X. So, it does not matter what XY is, any cell that sees (only) both of XYZ and XZ cannot be X.

Very cool. These are all ways to start from a basic pattern and then build a longer chain of eliminations. Which removes my basic objection to chains: How do you recognize them?

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Fri Nov 09, 2007 4:55 am    Post subject: Reply with quote
Quote:
If you solve this puzzle using a regular hierarchy of methods


That's a new term to me, "regular hierarchy of methods." I guess it implies some ordered way of looking for techniques, as opposed to the haphazard way that I go about it.

For example, in Asellus' position, the Type 6 on 78 jumps right off the page. Why not use it if it's there?
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Fri Nov 09, 2007 9:54 am    Post subject: Reply with quote
Keith wrote:
Very cool. These are all ways to start from a basic pattern and then build a longer chain of eliminations. Which removes my basic objection to chains: How do you recognize them?


My answer: spot the otherwise "useless" "basic pattern" and see if it can be extended somehow. The "somehow" might vary; but, realizing that it can vary is part of the process of enhancing ones solving abilities. (I might add that, while I personally have no objections to chains, this approach doesn't seem like a "chain" to me... though, of course, virtually any sudoku solving technique can be expressed as a chain, and so it is.)

Keith wrote:
If you solve this puzzle using a regular hierarchy of methods (from the position posted by Asellus) you will find an X-wing, an XY-wing, a Type 1 UR and a BUG+1.

Well, I beg to differ... not about the solution, but about the notion of "heirarchy." In my book, a Skyscraper has more heirarchy than a UR or any uniqueness method. But, maybe that's just a difference in heirarchies. In any case, the Skyscraper is on <5> in R57 and eliminates <5> from R6C5 and R8C6, solving the puzzle without any uniqueness-based methods.

Marty wrote:
For example, in Asellus' position, the Type 6 on 78 jumps right off the page. Why not use it if it's there?


No reason at all... except the reason that some folks object to uniqueness-based solutions. Also, that UR doesn't lead immediately to a solution and, so far at least, it isn't part of the shortest path to a solution, regardless of when and how it is invoked. However, like nataraj, I like scenic routes. And, I don't care how long they are. So, it's no problem for me.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Fri Nov 09, 2007 10:24 pm    Post subject: Reply with quote
Marty wrote:
For example, in Asellus' position, the Type 6 on 78 jumps right off the page. Why not use it if it's there?


No reason at all, if you're solving the puzzle for yourself. (Would it bother you that you missed the Squirmbag?) (Which is the complement of the easy to spot X-wing.)

But, a Type 6 UR is not implemented in any solver that I know, and is not explained in many guides. I was simply trying to explain what someone might find if they used some particular software as an aid.

The "hierarchy" thing is a little more difficult to deal with. Each of us has our own methodology to solve a tough puzzle. Personally, I go from naked and hidden singles to looking for pairs of strong links.

Strong links are a path to many things, including box-line interactions, X-wings, and skyscrapers. And, UR's, W-wings ...

Then, I will check for XY- and XYZ-wings. If that fails, it's time for the heavy artillery: Map out all the strong links (coloring).

So, I am generally with Marty. As Yogi Berra said: "If you come to a fork in the road, take it." Use whatever method works.

Except: For example, this site's Very Hards. We know they can be solved with only X-, XY-, and XYZ-wings. So, I will try to solve them that way. A UR or skyscraper may break the puzzle, but I will try to find the other solution path.

It's the journey.

Keith
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