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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Sat Feb 14, 2009 3:33 pm Post subject: Feb 14 DB |
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This DB Valentine for Sudoku lovers is a skyscraper in <8> (C4,9).
Earl
| Code: |
+-------+-------+-------+
| . 9 . | 3 . . | 7 2 . |
| . . 8 | . 2 . | 9 . . |
| . . 4 | . . . | . . 5 |
+-------+-------+-------+
| . . . | 9 . . | 1 7 . |
| 9 . 2 | . . . | 3 . 4 |
| . 8 1 | . . 3 | . . . |
+-------+-------+-------+
| 1 . . | . . . | 6 . . |
| . . 7 | . 3 . | 4 . . |
| . 2 6 | . . 7 | . 9 . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Feb 15, 2009 7:06 am Post subject: |
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I don't know how to do skyscrapers. Is there any other solution to this. We are stuck.  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Feb 15, 2009 9:41 am Post subject: |
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| sudocraz wrote: | | I don't know how to do skyscrapers. Is there any other solution to this. We are stuck. |
This puzzle really calls out for a Skyscraper/Empty Rectangle/2-String Kite to solve it. Here's the PM and candidate grid for <8>.
| Code: | after basics and before an X-Wing on <3>
*--------------------------------------------------------------------*
| 6 9 5 | 3 48 48 | 7 2 1 |
| 37 137 8 | 157 2 156 | 9 4 36 |
| 2 137 4 | 17 9 16 | 8 36 5 |
|----------------------+----------------------+----------------------|
| 45 46 3 | 9 4568 2 | 1 7 68 |
| 9 67 2 | 158 15678 158 | 3 568 4 |
| 457 8 1 | 45 4567 3 | 2 56 9 |
|----------------------+----------------------+----------------------|
| 1 34 9 | 2 458 458 | 6 38 7 |
| 8 5 7 | 6 3 9 | 4 1 2 |
| 34 2 6 | 148 148 7 | 5 9 38 |
*--------------------------------------------------------------------*
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| Code: | candidate grid for <8>
+-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . 8 . | . . 8 |
| . . . | 8 8 8 | . 8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . 8 8 | . 8 . |
| 8 . . | . . . | . . . |
| . . . | 8 8 . | . . 8 |
+-----------------------------------+
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Would you like to see examples of the three techniques I listed?
(No Ted, the Kraken X-Wing is not up for discussion  ) |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Sun Feb 15, 2009 4:56 pm Post subject: |
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Hi Daj
At the moment the Skyscraper is beyond my understanding. I would like to see an example of an Empty Rectangle though.
Regards
Sheila |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Feb 15, 2009 8:22 pm Post subject: |
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| sudocraz wrote: | At the moment the Skyscraper is beyond my understanding. I would like to see an example of an Empty Rectangle though.
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I love a challenge.
Skyscraper:
[c4] has strong link (*) and [c9] has strong link (@). [r9] contains a cell from each strong link. Now, let's alternately consider [r4c9] true/false for <8>. (The same logic would work for [r5c4])
| Code: | [r4c9]= 8 => [r4c5],[r5c8]<>8 (are among the eliminations)
[r4c9]<>8 [r9c9]=8 [r9c4]<>8 [r5c4]=8 => [r4c5],[r5c8]<>8 (are among the eliminations)
+-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . -8 . | . . @8 |
| . . . | *8 8 8 | . -8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . 8 8 | . 8 . |
| 8 . . | . . . | . . . |
| . . . | *8 8 . | . . @8 | <-- common row
+-----------------------------------+
^ ^
|-----------------| <-- two columns w/strong link
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Any cells that see the two non-aligned cells -- [r4c9] & [r5c4] -- can have <8> eliminated.
Now, let's turn the pattern upside down and have you find the eliminations for the second Skyscraper in this candidate grid.
| Code: | +-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . 8 . | . . 8 |
| . . . | *8 8 8 | . @8 . | <-- common row
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . 8 8 | . @8 . |
| 8 . . | . . . | . . . |
| . . . | *8 8 . | . . 8 |
+-----------------------------------+
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Final Note: This logic (obviously) works if two rows have strong links and a column contains a cell from each strong link. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Feb 15, 2009 8:59 pm Post subject: |
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2-String Kite:
[c4] has strong link (*) and [r4] has strong link (@). [b5] contains a cell from each strong link. Now, let's alternately consider [r4c9] true/false for <8>. (The same logic would work for [r9c4])
| Code: | [r4c9]= 8 => [r9c9]<>8 (is among the eliminations)
[r4c9]<>8 [r4c5]=8 [r5c4]<>8 [r9c4]=8 => [r9c9]<>8 (is among the eliminations)
+-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . @8 . | . . @8 | <- strong link in row
| . . . | *8 8 8 | . 8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------| [b5] common
| . . . | . 8 8 | . 8 . |
| 8 . . | . . . | . . . |
| . . . | *8 8 . | . . -8 |
+-----------------------------------+
^
| <- strong link in column
|
The one cell outside of [b5] -- [r9c9] -- that sees the two cells not in [b5] -- [r4c9] & [r9c4] -- can have <8> eliminated.
Now, let's have you find the elimination for a different 2-String Kite in this candidate grid.
| Code: | +-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------| [b6] is common
| . . . | . @8 . | . . @8 |
| . . . | 8 8 8 | . *8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . 8 8 | . *8 . |
| 8 . . | . . . | . . . |
| . . . | 8 8 . | . . 8 |
+-----------------------------------+
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Feb 15, 2009 9:07 pm Post subject: |
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Unfortunately, you asked for an example of the hardest technique to explain of the three. First, I need to know if you're comfortable with the subject of grouped strong links. If so, then send me a private message (pm) and I'll provide two examples grids like I did for each technique above.
Empty Rectangle (technique): currently on hold! |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Feb 15, 2009 10:25 pm Post subject: |
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| daj95376 wrote: | Unfortunately, you asked for an example of the hardest technique to explain of the three. First, I need to know if you're comfortable with the subject of grouped strong links. If so, then send me a private message (pm) and I'll provide two examples grids like I did for each technique above.
Empty Rectangle (technique): currently on hold! |
How about this? | Code: | candidate grid for <8>
+-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . 8 . | . . 8 |
| . . . | 8 8 8 | . 8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . 8 8 | . 8 . |
| 8 . . | . . . | . . . |
| . . . | 8 8 . | . . 8 |
+-----------------------------------+ |
Replacing some of the <8> candidates with other symbols: | Code: | 8 could occur in any of the cells marked @ and #.
+-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . a . | . . A |
| . . . | 8 8 8 | . 8 . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . * 8 | @ @ # |
| 8 . . | . . . | . . @ |
| . . . | 8 8 . | . . @ |
+-----------------------------------+ |
In B9, the candidates lie only in one row and one column. This row and column intersect at #. Also, there is a strong link aA, and a candidate *. Note that #* lines up with aA.
Now, if a is true, <8>, * is false.
If a is false, A is true, the <8> in B9 must lie in R7, and * is false.
Either way, * is false.
The way I look for them is:
Look at each box. Do any candidates lie only in one row and one column? If so, identify the # cell. Now, external to the box, is there a strong link in the same candidate, where one end lines up with #? If so, is there a cell * where an elimination can be made?
I hope this helps.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Feb 15, 2009 10:54 pm Post subject: |
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I notice another ER that makes the same elimination:
| Code: | +-----------------------------------+
| . . . | . 8 8 | . . . |
| . . 8 | . . . | . . . |
| . . . | . . . | 8 . . |
|-----------+-----------+-----------|
| . . . | . 8 . | . . 8 |
| . . . | 8 # 8 | . A . |
| . 8 . | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . * 8 | . a . |
| 8 . . | . . . | . . . |
| . . . | 8 8 . | . . 8 |
+-----------------------------------+ |
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Feb 16, 2009 1:20 am Post subject: |
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Here's an actual example. Note in box 1 the 8s intersect at r1c1 (this is called the ERI--Empty Rectangle Intersection). The ERI sees part of a strong link on 8 in row 9. The 8 in r1c5 sees both the ERI and the second half of the row 9 strong link, so that 8 gets eliminated.
| Code: | +-------------+------------------+-----------------+
| 7 58 123 | 4 12358 1358 | 6 9 2358 |
| 568 9 23 | 7 568 58 | 1 23 4 |
| 568 4 123 | 9 123568 1358 | 2578 237 23578 |
+-------------+------------------+-----------------+
| 4 157 8 | 15 9 2 | 3 167 67 |
| 3 2 6 | 18 4 178 | 78 5 9 |
| 15 157 9 | 6 1358 13578 | 4 127 278 |
+-------------+------------------+-----------------+
| 12 13 4 | 125 157 6 | 9 8 2357 |
| 9 138 5 | 128 178 4 | 27 2367 2367 |
| 28 6 7 | 3 58 9 | 25 4 1 |
+-------------+------------------+-----------------+ |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Mon Feb 16, 2009 2:14 am Post subject: |
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Hi Daj, Marty, Keith, Earl,
Thank you for all of your help. 
I will print all of this out and try to understand it.  Right now my repertoire, after basics, consists of: X-wing, UR 1, XY-Wing, XYZ Wing and Bug Removal 1.
Thanks again.
Sheila |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Feb 16, 2009 5:01 am Post subject: |
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Sheila,
Not that you asked my advice, but after the ER, if you're interested, I'd ask about UR 2 & 4, pincer transport and W- and M-Wings. Sounds like a lot, but no need to rush, you can digest them slowly, one at a time. |
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sudocraz
Joined: 28 Apr 2008
Posts: 53
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| Posted: Tue Feb 17, 2009 12:47 am Post subject: |
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Hi Marty,
You are probably right. I think that we will start examining the UR 2, 3 and 4. I have material on them that I haven't looked at yet. It is lots of fun learning new things.
Thanks
Sheila |
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