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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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 Posted: Tue May 20, 2008 6:39 pm Post subject: |
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No – I just don’t understand Type 4 URs when there are more than 3 candidates involved in any cell. Here in R6 we have 3 and 5.
I realise you can’t have this - because of the deadly thing.
| Code: |
+------------+
| . . . |
| . . . |
| 23 . 23 |
+------------+
| . . . |
| . . . |
| 23 . 23 |
+------------+
|
And I also realise there are only two <3>s in R6
But why can’t I have this: Or any number of variations – given that there are 5 available numbers in R6 and a urine potful of variables that do not provide the deadly thing shown above. My apologies – but I just don’t get it.
| Code: |
+--------------+
| . . . |
| . . . |
| 23 . 23 |
+--------------+
| . . . |
| . . . |
| 27 . 34 |
+--------------+
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue May 20, 2008 7:22 pm Post subject: |
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| cgordon wrote: | | But why can’t I have this |
Because your 34 would immediately collapse to a placed <3>. (This three is now a hidden single since you have removed the only other <3> in r6.) That would give you:
| Code: | +--------------+
| . . . |
| . . . |
| 3 . 2 |
+--------------+
| . . . |
| . . . |
| 27 . 3 |
+--------------+ |
by the cascading placements. Now, if the 27 is <2>, then you have the Deadly Pattern. So, it would have to be <7>. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue May 20, 2008 9:10 pm Post subject: |
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| Code: | +-------------------+-------------------+-------------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
+-------------------+-------------------+-------------------+
| 489 1 289 | 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478 |
| 6 5 27 | 9 8 24 | 237 14 12347 |
+-------------------+-------------------+-------------------+
| 789 3678 5 | 2 36 19 | 4 18 1678 |
| 2 678 789 | 5 4 19 | 78 3 1678 |
| 1 36 4 | 8 36 7 | 9 2 5 |
+-------------------+-------------------+-------------------+ |
Here are the explanations from Sudoku Susser:
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Squares R3C7, R3C9, R6C7 and R6C9 form a Type-4 Unique Rectangle on <23>. Because they share two rows, two columns, and two blocks, if they all had possibilities <23> then the puzzle would have two solutions; you could simply exchange the <2>s with the <3>s in the squares to get the other solution, and their common rows, columns and blocks would still contain one of each value. If you look carefully, you'll see that the only squares in block 6 that can contain <3> are the "roof" squares -- R6C7 and R6C9. Since one of these squares must be <3>, the only way to avoid the "deadly pattern" is if neither of them can contain <2>.
R6C7 - can remove <2> from <237> leaving <37>.
R6C9 - can remove <2> from <12347> leaving <1347>.
----
Squares R9C2, R9C5, R7C2 and R7C5 form a Type-1 Unique Rectangle on <36>. Because they share two rows, two columns, and two blocks, if they all had possibilities <36> then the puzzle would have two solutions; you could simply exchange the <3>s with the <6>s in the squares to get the other solution, and their common rows, columns and blocks would still contain one of each value. Since a valid Sudoku can have only one solution, R7C2 cannot contain <36>, since if it has either value, the other squares will immediately be forced into a two-solution configuration.
R7C2 - can remove <36> from <3678> leaving <78>.
----
I hope this helps.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue May 20, 2008 9:11 pm Post subject: |
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This Type 4 UR kind of reminds me of all those years ago when I did calculus. The only way I ever understood was by rote - though in truth it's probably the same now with wings and other stuff (except x wings and ER's).
So to apply a rote rule to Type 4 URs - if I get four 23s like this - and if there are only two <3>s in the two corners that have more numbers than 23 - I can say there are no 2's in those places.
Though I still have to figure the rule if the 23s are diagonal.
Apologies for being a Philistine.
Edited note: Thanks Keith - I posted before seeing your response.
| Code: |
+-------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | 23 . 23 |
+-------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | 237 . 12347|
+-------+-------+------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+------------+
|
Last edited by cgordon on Tue May 20, 2008 9:14 pm; edited 2 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue May 20, 2008 9:11 pm Post subject: |
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Craig,
Asellus covered it, but let me use the words by which I understand a Type 4:
| Code: | +-------------------+-------------------+-------------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
+-------------------+-------------------+-------------------+
| 489 1 289 | 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478 |
| 6 5 27 | 9 8 24 | 237 14 12347 |
+-------------------+-------------------+-------------------+
| 789 3678 5 | 2 36 19 | 4 18 1678 |
| 2 678 789 | 5 4 19 | 78 3 1678 |
| 1 36 4 | 8 36 7 | 9 2 5 |
+-------------------+-------------------+-------------------+ |
Of r6c79, one must be = 3, so the other can't be = 2 if we want to avoid the deadly pattern. So a 2 just can't be a candidate in those two cells. If one of those cells were = 2, then the other would have to be = 3 and you'd have the DP.
Ask more questions if you need to, because it's important; the Type 1 and Type 4 are the most commonly encountered URs. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue May 20, 2008 9:44 pm Post subject: |
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Thanks to you too Marty. But you say that the Type 1 and Type 4 are the most commonly encountered UR's. I've been involved in these forums a while now and I don't recall too many mentions of Type 4's. Though perhaps - as in this post - they have simply been referred to as UR's.
However I still get the feeling this is a very useful and under-used tool.
Last edited by cgordon on Wed May 21, 2008 12:19 pm; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue May 20, 2008 11:38 pm Post subject: |
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| Quote: | | Thanks to you too Marty. But you say that the Type 1 and Type 4 are the most commonly encountered UR's. |
Maybe I shouldn't generalize, but they're certainly the most common by far that I encounter. |
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