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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Tue Dec 21, 2010 11:55 pm Post subject: Rambling: DP ??? |
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Normally, I'd describe the following as two overlapping UR patterns. In light of recent discussions, I'm now tempted to describe it as a DP pattern.
| Code: | +-----------------------+
| . 3 . | 6 9 7 | . 5 . |
| . . . | 8 . . | 3 7 2 |
| . . 7 | 2 . 5 | . 9 . |
|-------+-------+-------|
| 3 6 . | . 7 . | 5 . . |
| 5 . . | 3 4 2 | . 1 6 |
| . 4 . | . 6 . | . 3 . |
|-------+-------+-------|
| . . . | . . . | 7 8 . |
| . 5 . | 7 . . | 1 . 3 |
| . . . | . . 3 | . . . |
+-----------------------+
after basics: w/ineffective DP ?
+--------------------------------------------------------------+
| 124 3 1248 | 6 9 7 | 48 5 148 |
| 6 9 5 | 8 1 4 | 3 7 2 |
| 148 18 7 | 2 3 5 | 6 9 148 |
|--------------------+--------------------+--------------------|
| 3 6 *18+2 | 9 7 *18 | 5 24 48 |
| 5 7 *89 | 3 4 2 | *89 1 6 |
| 189-2 4 *189+2 | 5 6 *18 | *89+2 3 7 |
|--------------------+--------------------+--------------------|
| 19 12 3 | 4 25 6 | 7 8 59 |
| 48 5 468 | 7 28 9 | 1 26 3 |
| 7 28 689 | 1 258 3 | 24 246 59 |
+--------------------------------------------------------------+
# 47 eliminations remain
|
| Code: | exclude the "+2" candidates: DP ?
+-----------------------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|---------------+---------------+---------------|
| . . 18 | . . 18 | . . . |
| . . 89 | . . . | 89 . . |
| . . 189 | . . 18 | 89 . . |
|---------------+---------------+---------------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------------------+
scenario r4c3=1 => <89> DP
+-----------------------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|---------------+---------------+---------------|
| . . 1 | . . 8 | . . . |
| . . 89 | . . . | 89 . . |
| . . 89 | . . 1 | 89 . . |
|---------------+---------------+---------------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------------------+
scenario r4c3=8 => <18> DP
+-----------------------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|---------------+---------------+---------------|
| . . 8 | . . 1 | . . . |
| . . 9 | . . . | 8 . . |
| . . 1 | . . 8 | 9 . . |
|---------------+---------------+---------------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------------------+
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Conclusion: ( r4c3,r6c7=2 or r6c3=2 ) => r6c1<>2
BTW: The solution to this puzzle does not contain a UR pattern anywhere!
| Code: | +-----------------------+
| 2 3 4 | 6 9 7 | 8 5 1 |
| 6 9 5 | 8 1 4 | 3 7 2 |
| 8 1 7 | 2 3 5 | 6 9 4 |
|-------+-------+-------|
| 3 6 2 | 9 7 1 | 5 4 8 |
| 5 7 8 | 3 4 2 | 9 1 6 |
| 9 4 1 | 5 6 8 | 2 3 7 |
|-------+-------+-------|
| 1 2 3 | 4 5 6 | 7 8 9 |
| 4 5 6 | 7 8 9 | 1 2 3 |
| 7 8 9 | 1 2 3 | 4 6 5 |
+-----------------------+
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Dec 22, 2010 1:55 am Post subject: |
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| Quote: | I used two flightless M-Wings and I don't recall if the first was needed.
M-Wing (24); r7c1<>4
M-Wing (48); r89c8<>4 |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Thu Dec 23, 2010 3:26 pm Post subject: |
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Danny
Resist the temptation!
All the graves I have seen, whether universal or light, bi- or multi-valent, share two characteristics. They imply that the pattern has no solution or gives rise to more than one solution and the implication is proved by assuming there is a solution and exhibiting a permutation of the candidates that derives a second solution from the first.
The uniqueness rectangle provides the simplest example:
| Code: | +-------------------------------------------------+
| ab . . | ab . . | . . . |
| . . . | . . . | . . . |
| ab . . | ab . . | . . . |
|-------------------------------------------------| |
This pattern always offers a solution unless a = b and transposing a and b preserves the candidates in each cell of the pattern so, whichever solution we start with, the transposition gives another.
Let’s try that with your pattern, repeated for convenience:
| Code: | +-----------------------------------------------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|---------------+---------------+---------------|
| . . 18 | . . 18 | . . . |
| . . 89 | . . . | 89 . . |
| . . 189 | . . 18 | 89 . . |
|---------------+---------------+---------------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------------------------------+ |
Assume there is a solution. Any permutation of the candidates which changes the solution in box 6 must transpose 1 and 8. However, this does not preserve the candidates in box 7. Similarly, transposing 8 and 9 (from box 7) doesn’t preserve the candidates in box 6. So no permutation can alter the solution in boxes 6 and 7/ that is, the only permutation available is the identity, fixing 1, 8 and 9. But then the solution on box 3 is unaltered as well.
There is a similar problem with a pattern which Ron calls a bivalent grave:
| Code: | . . . | . . . | ab ab .
ab ab . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. ac . | . . . | ac . .
. . . | . . ac | . ac .
ac . . | . . ac | . . .
----------+----------+----------
. bc . | . . . | . bc .
. . . | . . . | . . .
bc . . | . . . | bc . . |
Any permutation of (abc) which preserves the candidates in box 1 must be a transposition of a and b, so leaving c fixed and altering the candidates in box 3 to bc. Similarly, any permutation which preserves box 3 alters the candidates in box 1.
The two patterns concerned may be useful to solvers. If they are, they deserve a name. My argument is that the underlying structure differs so markedly from what up to now have been called deadly patterns/graves that a different name is required.
Steve |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Thu Dec 23, 2010 9:56 pm Post subject: |
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| I am surprised to hear an objection to Danny's MUG which looks like a canonical example to me! (But what do I know!) This thread on the players forum gives the case of two overlapping UR's as its first example here. I don't know if this is the first discussion on MUGs - probably not. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Fri Dec 24, 2010 1:13 am Post subject: |
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| Steve R wrote: | There is a similar problem with a pattern which Ron calls a bivalent grave:
| Code: | . . . | . . . | ab ab .
ab ab . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. ac . | . . . | ac . .
. . . | . . ac | . ac .
ac . . | . . ac | . . .
----------+----------+----------
. bc . | . . . | . bc .
. . . | . . . | . . .
bc . . | . . . | bc . . |
Any permutation of (abc) which preserves the candidates in box 1 must be a transposition of a and b, so leaving c fixed and altering the candidates in box 3 to bc. Similarly, any permutation which preserves box 3 alters the candidates in box 1. |
Who or what says that is a requirement?
Better yet, have you a counter-example, preferably with pencilmarks from an actual puzzle, that shows such an application of the BUG rule leading to an invalid elimination? |
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