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February 3 VH

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sun Feb 03, 2008 5:07 pm    Post subject: February 3 VH Reply with quote

There it was, we're back in business. But I couldn't find a February 1 or 2.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Sun Feb 03, 2008 5:45 pm    Post subject: Reply with quote

back in business, and a good solid vh.


Not quite easy to spot x-wing (5) and then xy-wing 46-24-26 did it.
Looking forward to seeing other solutions.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sun Feb 03, 2008 8:13 pm    Post subject: Reply with quote

Quote:
Looking forward to seeing other solutions.

OK, this is other, but not better. It didn't come easy. Started with a Type 4 UR on 17. Then multi-coloring on 1. Then an XY-Wing on 24-12-14 with pincer coloring. A search for X-Wings/skyscrapers came up empty. I thought I'd need to try Medusa, but first I tried ER's and had one on 6 which broke it open.

A vh VH because I obviously missed something.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sun Feb 03, 2008 9:16 pm    Post subject: Reply with quote

After the basics, I found a finned x-wing to delete a <5> at r8c5, but I am not sure that really helped because coloring on <6> resulted in six deletions that broke the puzzle open.

Ted
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Mindwarp



Joined: 13 Sep 2007
Posts: 25
Location: St. Ives, England

PostPosted: Sun Feb 03, 2008 10:46 pm    Post subject: Reply with quote

Ah we are back, unfortunately for me it is one of those VH's for which will have to go in the unsolved archive. I just don't have the techniques for solving this variety. All I do is stare at it for ages not able to see any way through. Sad
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Sun Feb 03, 2008 11:02 pm    Post subject: Reply with quote

When the grid is loaded with multivalue cells after basics, first thing I search for are some ER's, being a P&P solver I find these ER's easier to find than

an x-wing, but that's just from one's own experience, because they sometimes overlap x-wings and finned x-wings, others may find x-wings easier too spot.

An ER for digit <6> in Box 1 takes out <6> in R5C1, the eri(Empty Rectangle Intersection) in R1C1 can see one of the strong link* on <6> in C6, collapsing

the whole puzzle.
Code:
+--------------------------+--------------------------+--------------------------+
| 5 eri     234      2369  | 17         1267   * 126  | 8         2349      234  |
| 239    er 7    er  239   | 4          8        5    | 6         239       1    |
| 246    er 8    er  1     | 9          26       3    | 7         5         24   |
+--------------------------+--------------------------+--------------------------+
| 34        345      7     | 2          9        14   | 135       8         6    |
| 234-[6]9  2345     2369  | 8          1456   * 146  | 12359     23        7    |
| 8         1        269   | 56         3        7    | 259       24        245  |
+--------------------------+--------------------------+--------------------------+
| 12        6        5     | 3          12       9    | 4         7         8    |
| 7         9        4     | 56         256      8    | 235       1         235  |
| 123       23       8     | 17         12457    124  | 25        6         9    |
+--------------------------+--------------------------+--------------------------+
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Mon Feb 04, 2008 2:01 am    Post subject: Reply with quote

x-wing on 5

coloring on 6

SE 4.2
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Mon Feb 04, 2008 6:50 am    Post subject: Reply with quote

Mindwarp wrote:
Ah we are back, unfortunately for me it is one of those VH's for which will have to go in the unsolved archive. I just don't have the techniques for solving this variety. All I do is stare at it for ages not able to see any way through. Sad


Mindwarp, I am sure you are not the only one. This puzzle is somewhat more difficult than the usual VHs, because the more obvious singles and naked pairs don't go as far as usual.

After basics, this is what you should have:
Code:

+--------------------------+--------------------------+--------------------------+
| 5       234     2369     | 17      1267    126      | 8       2349    234      |
| 239     7       239      | 4       8       5        | 6       239     1        |
| 246     8       1        | 9       26      3        | 7       5       24       |
+--------------------------+--------------------------+--------------------------+
| 34      345     7        | 2       9       14       | 135     8       6        |
| 23469   2345    2369     | 8       1456    146      | 12359   23      7        |
| 8       1       269      | 56      3       7        | 259     24      245      |
+--------------------------+--------------------------+--------------------------+
| 12      6       5        | 3       12      9        | 4       7       8        |
| 7       9       4        | 56      256     8        | 235     1       235      |
| 123     23      8        | 17      12457   124      | 25      6       9        |
+--------------------------+--------------------------+--------------------------+


If you have more candidates in some cells, you are probably missing a triple or a box/line interaction.

But even if you got here clean, there are many cells with more than two candidates, and the search for xy-wings doesn't turn up any results at this point.

This is when looking for x-wings or similar patterns become necessary.

What I do is, I take each number (1,2,3...) in turn (actually I start with those that already have many solved cells - it is easier to spot patterns if only few cells remain ...)

Let's see, what we have:
"many": 8 (9 solved), 7 (7 solved)
"some": 1,5,6 (4 solved) 3 (3)
"few": 2 (only 1 solved)

8 is fully soved - nothing to do

7 is almost solved, only r19c45 remain. This is the x-wing pattern we are looking for: 4 cells in a square. Unfortunately, if there are no other cells with this number (7) in it, there is nothing else to do. But remember the pattern - two rows with 2 sevens each, and at the same columns. Or two columns with 2 sevens each, and at the same rows.

I gave the clue in my previous post, so let's look at "5".

The rows yield nothing - a few rows with only 2 fives, but at wildly different column positions.

But the columns: There are 3 columns with exactly two 5s: cols 2,4,9.

In columns 4 and 9, the fives are at rows 6 and 8.

Heureka! The x-wing pattern! It means that in rows 6 and 8 the two "5"s must be at columns 4 and 9. Thus we can eliminate "5" from all the other columns in those two rows.

That removes 5 from r4c7 and r8c5 and r8c7.

I remember I used to look at the grid forever in those situations. What I found out is that one needs a search pattern. It is much too frustrating to look at the same cells over and over again - only to realize later that the solution was there all the time but I did not know what to look for.

So try this
a) Do a rough estimate (for each number 1,2,3...) of how many cells are SOLVED with that number. "rough" means "many", "some", "few"
b) Start with the "many". Look for rows with only 2 occurrences of that number. Look for the xwing pattern. Do the same for columns.
c) Work your way down to "some" and "few".
d) Even if nothing was found, at that point you KNOW there are no x-wings and something else is needed. Coffe break, most probably Wink

It is a bit tedious. But does NOT take very long. We are talking 5-10 minutes for a whole puzzle, max. And it beats staring at the thing "for ages" Smile anytime.

And - psychologically speaking - this strategy (or any other structured search pattern) gives one the feeling of being in control, of having a plan. And that is much much better than a random search...

_____

Just for the record: if we had continued with "6", we would have found nothing with this simple search pattern. The "skyscraper" pattern (two rows with 2 candidates each but ony with ONE position shared) in columns 1 and 6 is only slightly more difficult to spot (in this case it allows to remove 6 from r1c3 and r3c5), the "kite", "turbot fish" and other patterns (so called "coloring" techniques, or the Empty Rectangle in Johan's post) need differnt searches.
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melis



Joined: 04 Feb 2008
Posts: 6
Location: Berkshire, England

PostPosted: Mon Feb 04, 2008 9:29 am    Post subject: Thanks, Nataraj Reply with quote

Although I've been doing sudoku for a year or so, I'm a newbie with terms and techniques having only recently discovered sudoku online. A big thank you to for your 'tutorial'. It's not the techniques but finding the patterns that I find challenging and your advice was extremely useful. Now I have a plan....bring on those VH!!
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melis



Joined: 04 Feb 2008
Posts: 6
Location: Berkshire, England

PostPosted: Mon Feb 04, 2008 12:49 pm    Post subject: Feb 3 VH Reply with quote

OK, got the 5 x-wing and cleaned it up a bit, but am stuck again! Just don't want to give up, otherwise I'm never going to learn. Any advice? Confused
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Feb 04, 2008 1:45 pm    Post subject: Reply with quote

There is one more advanced step needed (i suppose you noticed the pairs and had some singles).
Code:
 *-----------------------------------------------------*
 | 5     24   2369  | 1   7   26   | 8      2349  234  |
 | 39    7    239   | 4   8   5    | 6      239   1    |
 | 46    8    1     | 9   26  3    | 7      5     24   |
 |------------------+--------------+-------------------|
 | 34    45   7     | 2   9   14   | 135    8     6    |
 | 3469  245  2369  | 8   45  146  | 12359  23    7    |
 | 8     1    269   | 56  3   7    | 29     24    245  |
 |------------------+--------------+-------------------|
 | 2     6    5     | 3   1   9    | 4      7     8    |
 | 7     9    4     | 56  26  8    | 23     1     235  |
 | 1     3    8     | 7   45  24   | 25     6     9    |
 *-----------------------------------------------------*

In boxes 1 and 2 you can find 2 xy-wings. Both solve the puzzle.
Alternatively you have Johan's ER or the skyscraper in 6 (columns 1 and 6).
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Mon Feb 04, 2008 4:19 pm    Post subject: Reply with quote

Again, it is helpful to use a search pattern.

Try this on for size:

Starting at the top left, take one row at a time, going from left to right, and look for bi-value cells (those cells with exactly two candidates in them).

In ravel's grid, the first such cell would be r1c2 {2,4}

For each cell found, look
- to the right in the same row
- down in the same column
- in the same box
and see if there are any other bi-value cells that share one candidate with the first cell found

In ravel's grid, that "second cell" would be r1c6 {2,6}

Now we need to look for the third cell that makes up the xy-wing. And as it happens, we know exactly what to look for: a cell with {4,6} in it that "sees" either the first or the second cell. We don't have to look far:
- row 1,
- columns 2,6
- boxes 1,2

Now, aren't we lucky today? r3c1 is such a cell! And we have found an xy-wing. Remains to see whether it solves anything: this xy-wing (46-24-26) removes 6 from all cells that see r3c1 and r1c6, and that would be r1c3 and r3c5. r3c5 is especially valuable, because it solves a cell r3c5=2.

Usually, at this point the search stops and we solve the sudoku.

Just for demonstration purposes, let us continue the search pattern.

There are no more cells with {4,6}

Look for other "second cells":
- nothing in row 1
- {4,5} in col 2 (r4c2). Look for {2,5}. No such luck
- {4,6} in box 1 r3c1. Look for {2,6) ... r1c5, we got that. r3c5 is good!

We found another xy-wing. This xy-wing (24-46-26) removes 2 from all cells that see r1c2 and r3c5, there is only one such cell r1c6 and it solves r1c6=6

No more second cells can be found, continue with all other possible first cells:

Take {2,6} in r1c6. The search becomes progressively faster because we only need to look right and down and box, not left and up (we already did these).

Possible "second cells": only one.
{2,4} (r9c6), with third cell {4,6}: such a cell exists, but not in rows 1,9, col 6 or boxes 2,8 -> no wing

Next "first cell": [3,9} in r2c1.
Second cells: none in r2, {3,4} in c1 (but no third cell {4,9}), none in box 1.

And so on.

A simple search pattern, guaranteed to find xy-wings if any exist.
And fast. The long explanation may look forbidding, but with a little practice it takes only a few minutes for the whole puzzle.

Only a little longer if one includes xyz-wings in the search.

Good hunting! Waidmannsheil!
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George Woods



Joined: 28 Mar 2006
Posts: 303
Location: Dorset UK

PostPosted: Mon Feb 04, 2008 5:52 pm    Post subject: w wing Reply with quote

Taking Ravel's grid there is a simple W wing - the 24s in boxes 1 and 3 acting on row 2! It then falls out!

The difficulty for me is getting to Ravel's grid!
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Wendy W



Joined: 04 Feb 2008
Posts: 144

PostPosted: Mon Feb 04, 2008 11:19 pm    Post subject: Reply with quote

Thank you, Nataraj! I completely overlooked that vertical x-wing on the 5's.
Good VH puzzle for Super Bowl Sunday.
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