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d_kahane
Joined: 09 Apr 2009
Posts: 4
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 Posted: Mon Jul 20, 2009 11:42 pm Post subject: 16-Apr-08 VH |
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Once again I'm staring and not seeing something potentially obvious. Can someone share a next step and a "why"? I am grateful for any help.
Link to image should appear above... |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Tue Jul 21, 2009 12:31 am Post subject: April VH |
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d.Kahane,
There is an xy-wing (247) which eliminates the 2 in R7C3.
If that doesn't solve it, look for another xy-wing in the upper tier.
Earl |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jul 21, 2009 1:16 am Post subject: |
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| Before the XY-Wings, there is a 48 pair in box 8. Not sure how far the cleanup from that would take you. |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Tue Jul 21, 2009 1:30 am Post subject: Re: 16-Apr-08 VH |
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| d_kahane wrote: | Once again I'm staring and not seeing something potentially obvious. Can someone share a next step and a "why"? I am grateful for any help.
Link to image should appear above... |
The 48 in column 6 is an 8 because of whatchacallit line-reduction? With that there are other numbers to remove. |
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d_kahane
Joined: 09 Apr 2009
Posts: 4
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| Posted: Tue Jul 21, 2009 4:34 am Post subject: |
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| Marty R. wrote: | | Before the XY-Wings, there is a 48 pair in box 8. Not sure how far the cleanup from that would take you. |
Yeah - that was a major typo. that's a 46 in that spot, not 48. sorry! I'm doing it on paper and transcribing to the online tool. |
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gindaani
Joined: 06 Mar 2009
Posts: 79
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| Posted: Tue Jul 21, 2009 8:09 pm Post subject: |
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You made a mistake somewhere prior to your picture. Some of your numbers conflict with the solution to the Apr 16 2008 puzzle.
PS If you use the "Play Online" button on this site, you can click "Ascii" to get a pop-up window with text to paste into the forums. This is easier than a screen shot, and it allows us to easily play from where you are.
Last edited by gindaani on Tue Jul 21, 2009 8:20 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Jul 21, 2009 8:15 pm Post subject: |
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Here is the puzzle: | Code: | +-------+-------+-------+
| 2 . . | 1 . . | 7 . . |
| . . 7 | 2 5 . | 4 . . |
| . 4 . | . . 8 | . . . |
+-------+-------+-------+
| . 9 3 | . 1 . | . . 8 |
| . . . | 4 . 2 | . . . |
| 5 . . | . 3 . | 1 6 . |
+-------+-------+-------+
| . . . | 9 . . | . 5 . |
| . . 6 | . 2 7 | 9 . . |
| . . 9 | . . 1 | . . 6 |
+-------+-------+-------+ |
After basics: | Code: | +-------------------+-------------------+-------------------+
| 2 368 58 | 1 469 346 | 7 389 359 |
| 13689 1368 7 | 2 5 36 | 4 1389 139 |
| 139 4 15 | 37 79 8 | 6 1239 12359 |
+-------------------+-------------------+-------------------+
| 47 9 3 | 6 1 5 | 2 47 8 |
| 1678 1678 18 | 4 78 2 | 5 39 39 |
| 5 278 24 | 78 3 9 | 1 6 47 |
+-------------------+-------------------+-------------------+
| 13478 12378 24 | 9 468 346 | 38 5 27 |
| 38 358 6 | 358 2 7 | 9 14 14 |
| 3478 23578 9 | 358 48 1 | 38 27 6 |
+-------------------+-------------------+-------------------+ |
There is a UR and an XY-wing here.
Keith |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Wed Jul 22, 2009 1:34 am Post subject: |
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| gindaani wrote: |
PS If you use the "Play Online" button on this site, you can click "Ascii" to get a pop-up window with text to paste into the forums. This is easier than a screen shot, and it allows us to easily play from where you are. |
Yes, yes, yes, here is the puzzle after the basics (according to me) removed. You can click this grid and play it yourself. This is the way to do it, so that we can all play from your point to ponder. I got an xy wing at this point: 2-4-7, where 47 is the pivot. Now I was not able to finish the puzzle with this alone. I needed another xy wing after this.
| Code: |
+----------------+-------------+---------------+
| 2 368 58 | 1 469 346 | 7 389 359 |
| 13689 1368 7 | 2 5 36 | 4 1389 139 |
| 139 4 15 | 37 79 8 | 6 1239 12359 |
+----------------+-------------+---------------+
| 467 9 3 | 67 1 5 | 2 47 8 |
| 1678 1678 18 | 4 678 2 | 5 39 39 |
| 5 278 24 | 78 3 9 | 1 6 47 |
+----------------+-------------+---------------+
| 13478 12378 24 | 9 468 346 | 38 5 27 |
| 38 358 6 | 358 2 7 | 9 14 14 |
| 3478 23578 9 | 358 48 1 | 38 27 6 |
+----------------+-------------+---------------+
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Play this puzzle online at the Daily Sudoku site
Here is where I landed after eliminations after the 2-4-7 xy-wing. I found another xy wing to finish the puzzle. Both of these puzzles you can play online, with a click on the blue words.
| Code: |
+------------+-----------+----------+
| 2 36 8 | 1 69 4 | 7 39 5 |
| 369 1 7 | 2 5 36 | 4 8 39 |
| 39 4 5 | 37 79 8 | 6 1 2 |
+------------+-----------+----------+
| 4 9 3 | 6 1 5 | 2 7 8 |
| 678 678 1 | 4 78 2 | 5 39 39 |
| 5 78 2 | 78 3 9 | 1 6 4 |
+------------+-----------+----------+
| 1 2 4 | 9 68 36 | 38 5 7 |
| 38 358 6 | 358 2 7 | 9 4 1 |
| 378 3578 9 | 358 4 1 | 38 2 6 |
+------------+-----------+----------+
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Play this puzzle online at the Daily Sudoku site |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Wed Jul 22, 2009 2:13 am Post subject: |
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I am not seeing the UR here. Can you elaborate?
| keith wrote: | Here is the puzzle: | Code: | +-------+-------+-------+
| 2 . . | 1 . . | 7 . . |
| . . 7 | 2 5 . | 4 . . |
| . 4 . | . . 8 | . . . |
+-------+-------+-------+
| . 9 3 | . 1 . | . . 8 |
| . . . | 4 . 2 | . . . |
| 5 . . | . 3 . | 1 6 . |
+-------+-------+-------+
| . . . | 9 . . | . 5 . |
| . . 6 | . 2 7 | 9 . . |
| . . 9 | . . 1 | . . 6 |
+-------+-------+-------+ |
After basics: | Code: | +-------------------+-------------------+-------------------+
| 2 368 58 | 1 469 346 | 7 389 359 |
| 13689 1368 7 | 2 5 36 | 4 1389 139 |
| 139 4 15 | 37 79 8 | 6 1239 12359 |
+-------------------+-------------------+-------------------+
| 47 9 3 | 6 1 5 | 2 47 8 |
| 1678 1678 18 | 4 78 2 | 5 39 39 |
| 5 278 24 | 78 3 9 | 1 6 47 |
+-------------------+-------------------+-------------------+
| 13478 12378 24 | 9 468 346 | 38 5 27 |
| 38 358 6 | 358 2 7 | 9 14 14 |
| 3478 23578 9 | 358 48 1 | 38 27 6 |
+-------------------+-------------------+-------------------+ |
There is a UR and an XY-wing here.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jul 22, 2009 3:22 am Post subject: |
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There is a Type 3 UR <39> which has a pair <58> in R1. It eliminates <8> from R1C2.
I have no idea if it solves the puzzle. I was simply suggesting a possible next move.
Best wishes,
Keith |
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crunched
Joined: 05 Feb 2008
Posts: 168
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| Posted: Wed Jul 22, 2009 11:07 am Post subject: |
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Thanks for explaining where the UR is. I wondered if the UR was a type other than 1. This gives me an inkling how a type 3 works. Not sure I would ever find one on my own though.
| keith wrote: | There is a Type 3 UR <39> which has a pair <58> in R1. It eliminates <8> from R1C2.
I have no idea if it solves the puzzle. I was simply suggesting a possible next move.
Best wishes,
Keith |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Sat Jul 25, 2009 12:29 am Post subject: |
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| crunched wrote: | This gives me an inkling how a type 3 works. Not sure I would ever find one on my own though.
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I'll bet you a buck you can  . Type 3s are not that common, but they stick out pretty readily if you isolate the extras ala our buddy storm_norm.
Step 1.) Look for locked pairs like the (39) in row 5.
Step 2.) If there's a potential deadly pattern there, isolate the extras, in this case 5 and 8 (edit: there can be more than two, see below)
Step 3.) See if both the extras are in a bivalue cell elsewhere in the same house (like the 58 in box one.)
| Code: | +-------------------+-------------------+-------------------+
| 2 36-8 *58 | 1 469 346 | 7 *39+8 *39+5 |
| 13689 1368 7 | 2 5 36 | 4 1389 139 |
| 139 4 15 | 37 79 8 | 6 1239 12359 |
+-------------------+-------------------+-------------------+
| 47 9 3 | 6 1 5 | 2 47 8 |
| 1678 1678 18 | 4 78 2 | 5 *39 *39 |
| 5 278 24 | 78 3 9 | 1 6 47 |
+-------------------+-------------------+-------------------+
| 13478 12378 24 | 9 468 346 | 38 5 27 |
| 38 358 6 | 358 2 7 | 9 14 14 |
| 3478 23578 9 | 358 48 1 | 38 27 6 |
+-------------------+-------------------+-------------------+ |
The eliminations: any 5 or 8 that can see both the extras and the bivalue cell.
Now, if you're game, check out Danny's Puzzle NR_063 below.
| Code: | *--------------------------------------------------------------------*
| 6 3 4 | 12 8 12 | 7 5 9 |
| 9 2 5 | 4 7 6 | 8 1 3 |
| 8 7 1 | 5 39 39 | 24 6 24 |
|----------------------+----------------------+----------------------|
| 127 6 9 | 1237 4 5 | 123 23 8 |
| 5 8 237 | 1237 6 12 | 12349 49 24 |
| 12 4 23 | 1239 29 8 | 6 7 5 |
|----------------------+----------------------+----------------------|
| 27 5 8 | 6 239 379 | 2349 49 1 |
| 3 1 6 | 29 5 4 | 29 8 7 |
| 4 9 27 | 8 1 37 | 5 23 6 |
*--------------------------------------------------------------------* |
Do I owe you a buck 
Last edited by Luke451 on Sat Jul 25, 2009 11:22 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 25, 2009 2:52 am Post subject: |
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> | Quote: | | Step 2.) If there's a potential deadly pattern there, isolate the extras, in this case 5 and 8 (there can't be more than two.) |
Not correct. I believe that theoretically, there may be up to five. I believe I have seen 4. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Sat Jul 25, 2009 5:57 am Post subject: |
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| keith wrote: | > | Quote: | | Step 2.) If there's a potential deadly pattern there, isolate the extras, in this case 5 and 8 (there can't be more than two.) |
Not correct. I believe that theoretically, there may be up to five. I believe I have seen 4. |
Hi, Keith. Well, leave it to me to get a detail wrong! Can you provide some examples? My references may be dated:
Havard, from here: | Quote: | | Type 3: UR with two extra candidates in addition to the UR-pair. Can create a locked set with other cells, as long as all the UR-extra-candidates-cells are concidered one cell in the locked set, and of course all cells in the locked set can see eachother... |
Ronk's synopsis, from here: | Quote: | | Type 3: two UR cells in a line, each with at most two identical candidates. |
Andrew Stuart from here: | Quote: | | In this variant we have a floor with a pair as before but the roof contains two different candidates (occurring once or twice in each cell of the roof). |
However, Sudopedia has a definition which may be where you're heading:
| Quote: | | Suppose both ceiling cells have extra candidates. By treating these two cells as one node, find k - 1 other cells (as nodes) in the same house as these two cells so that the union of the candidates for these k cells has exactly k unique digits. Then the Naked Subset rule can be applied eliminate these k digits from the other cells in the house. A rectangle that meets this test is also called a Type 3 Unique Rectangle. |
This sounds like the door is open to larger sets. For example, say the two UR cells contained three extra candidates, XYZ, and two other cells in the house contained XY and XZ. This would create a naked set and eliminate any other XYZ in the same house.
Perhaps for practical purposes (and the purposes of this discussion), "two extra candidates" is the norm, but more are theoretically possible and can occur on rare occasions. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 25, 2009 7:57 pm Post subject: |
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| Quote: |
Hi, Keith. Well, leave it to me to get a detail wrong! Can you provide some examples? |
Luke,
I don't have one at hand, but will point it out when I see it.
Let's say the deadly candidates are <12> and in the "roof" cells of the UR we have
There is no reason we cannot form a Type 3 if we find, for example, in the same row, column or box as the roof cells:
I have also seen a case where there is a candidate in the subset that is not in the UR. For example:
The restriction of two candidates is true if you are only looking for one cell to complete the subset. In this case the roof cells of the UR must be
and the subset is completed by a cell <34>.
Best wishes,
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Jul 25, 2009 9:57 pm Post subject: |
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I remember this post knocking my socks off for a UR Type 3.
Now that I review it, I think that Keith forgot to include [r4c4]=356. His list includes the pseudo-cell and four other cells to comprise a sextet of candidates. |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Sat Jul 25, 2009 11:20 pm Post subject: |
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Very cool. I will amend my post.
Does this mean I lose my bet? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jul 26, 2009 1:29 am Post subject: |
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Danny,
Thank you for remembering this! An incredible example! I believe your correction of my post is correct. (As always, my brain is missing a cell or two.)
| Luke451 wrote: | Very cool. I will amend my post.
Does this mean I lose my bet? |
Luke,
Yes. The next time you are in Detroit, I will buy you lunch. You use your dollar to help pay the tip.
Best wishes,
Keith
Last edited by keith on Sun Jul 26, 2009 2:01 am; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jul 26, 2009 1:56 am Post subject: |
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Not to gloat, but I will.
This Type-3 UR example is more general than any of those defined in the references quoted by Luke451.
To wit:
1. The subset may include more than two candidates.
2. The subset may include candidates not in the UR cells.
I have never thought of this other than: The extra candidates on the UR roof are a pseudo-cell. How can you use them?
Luke, and Danny,
Thank You!
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jul 26, 2009 4:45 pm Post subject: |
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Another example of a UR Type 3 w/three extra candidates -- from Mike Barker's contributions to the zoo. It shows that fewer cells (@) are possible to complete the subset. (There are three basic URs present.)
| Code: | +-----------------------+
| . . . | 5 . 1 | . . 3 |
| 2 . 9 | . . 4 | 8 . . |
| . 4 . | . . . | 5 . . |
|-------+-------+-------|
| . 1 . | 9 6 . | . . . |
| . . 2 | . . . | 1 . . |
| . . . | . 1 7 | . 8 . |
|-------+-------+-------|
| . . 8 | . . . | . 2 . |
| . . 3 | 4 . . | 7 . 6 |
| 5 . . | 7 . 9 | . . . |
+-----------------------+
r1 b1 Locked Triple <> 678 [r1c578]
c5b8 Locked Candidate 1 <> 3 [r2c5]
c7b9 Locked Candidate 1 <> 3 [r4c7]
c6b5 Locked Candidate 1 <> 5 [r8c6]
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| Code: | +--------------------------------------------------------------+
| 67 8 67 | 5 29 1 | 249 @49 3 |
| 2 5 9 | 3 7 4 | 8 6 1 |
| 3 4 1 | 6 289 28 | 5 @79 279 |
|--------------------+--------------------+--------------------|
| 8 1 457 | 9 6 *35 | 24 *35+47 2457 |
| 679 679 2 | 8 4 *35 | 1 *35+79 579 |
| 49 3 45 | 2 1 7 | 6 8 459 |
|--------------------+--------------------+--------------------|
| 479 79 8 | 1 35 6 | 349 2 459 |
| 1 29 3 | 4 258 28 | 7 5-9 6 |
| 5 26 46 | 7 23 9 | 34 1 8 |
+--------------------------------------------------------------+
# 53 eliminations remain
r38c56 <28> UR Type 4 <> 2 [r38c5] extraneous
r45c68 <35> UR Type 4 <> 5 [r45c8] crack!
r45c68 <35> UR Type 3 + <479> <> 9 [r8c8] crack!
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Interesting how there is an overlapping UR Type 4 in this example and in Keith's example. Probably just a coincidence. |
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