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Free Press May 11, 2012
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat May 12, 2012 4:03 pm    Post subject: Free Press May 11, 2012 Reply with quote

Code:
Puzzle: FP 051112
+-------+-------+-------+
| . 8 . | . . . | 4 . 6 |
| . . . | 7 3 . | 2 . . |
| 2 . . | . . . | 7 . . |
+-------+-------+-------+
| 1 . . | . 6 . | . . 7 |
| . 3 . | . . . | . 6 . |
| 7 . . | . 2 . | . . 1 |
+-------+-------+-------+
| . . 9 | . . . | . . 8 |
| . . 8 | . 5 6 | . . . |
| 5 . 4 | 2 . . | . . . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Keith
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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Sat May 12, 2012 5:36 pm    Post subject: Reply with quote

Code:
 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | 1     49    25    | 3489  6     345   | 38    2459  7     |
 | 8     3     25    | 149 ab479   1457  |b59    6    a24    |
 | 7     49    6     | 3489  2     345   | 38    459   1     |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134  a47    1347  | 15    2457  8     |
 | 3     127   8     | 1-49  5     6     |b19    2479 a24    |
 | 5     17    4     | 2    b789   178   | 6     79    3     |
 *-----------------------------------------------------------*
pair of skyscrapers remove 4 and 9 from r8c4; stte


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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat May 12, 2012 6:07 pm    Post subject: Reply with quote

arkietech wrote:
Code:
 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | 1     49    25    | 3489  6     345   | 38    2459  7     |
 | 8     3     25    | 149 ab479   1457  |b59    6    a24    |
 | 7     49    6     | 3489  2     345   | 38    459   1     |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134  a47    1347  | 15    2457  8     |
 | 3     127   8     | 1-49  5     6     |b19    2479 a24    |
 | 5     17    4     | 2    b789   178   | 6     79    3     |
 *-----------------------------------------------------------*
pair of skyscrapers remove 4 and 9 from r8c4; stte

The 4 SS only becomes apparent after you apply the 9 SS and simplify.

Keith

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arkietech



Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA

PostPosted: Sat May 12, 2012 6:40 pm    Post subject: Reply with quote

keith wrote:
The 4 SS only becomes apparent after you apply the 9 SS and simplify.

Your are right, my eyes have a hard time seeing what I don't want to see. Embarassed
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Clement



Joined: 24 Apr 2006
Posts: 1111
Location: Dar es Salaam Tanzania

PostPosted: Sat May 12, 2012 8:24 pm    Post subject: Free Press May 11, 2012 Reply with quote

Also Type 4 UR 38; r46c4<>3 and
a kite on 9 originating from BOX 9; r5c5<>9 which opens a skyscraper originating from r5c59; r7c8<>4.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Sat May 12, 2012 8:44 pm    Post subject: Reply with quote

Just in the pursuit of MUG fun, here's a bigun.
Code:
 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | 1    *49    25    |*3489  6    *345   |*38   *459+2 7     |
 | 8     3     25    | 149   479   1457  | 59    6     24    |
 | 7    *49    6     |*3489  2    *345   |*38   *459   1     |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134   47    1347  | 15    2457  8     |
 | 3     127   8     | 149   5     6     | 19    2479  24    |
 | 5     17    4     | 2     789   178   | 6     79    3     |
 *-----------------------------------------------------------*
MUG(34589)r46c24678 ==>r4c8=2

Naturally, it would've been a lot more fun had it solved the puzzle...
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tlanglet



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

PostPosted: Sat May 12, 2012 11:14 pm    Post subject: Reply with quote

Luke451 wrote:
Just in the pursuit of MUG fun, here's a bigun.
Code:
 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | 1    *49    25    |*3489  6    *345   |*38   *459+2 7     |
 | 8     3     25    | 149   479   1457  | 59    6     24    |
 | 7    *49    6     |*3489  2    *345   |*38   *459   1     |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134   47    1347  | 15    2457  8     |
 | 3     127   8     | 149   5     6     | 19    2479  24    |
 | 5     17    4     | 2     789   178   | 6     79    3     |
 *-----------------------------------------------------------*
MUG(34589)r46c24678 ==>r4c8=2

Naturally, it would've been a lot more fun had it solved the puzzle...

Fantastic Exclamation Exclamation

I just love "one time in your life" type moves.

Ted
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Marty R.



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

PostPosted: Sat May 12, 2012 11:18 pm    Post subject: Reply with quote

If there's a longer way, I can usually find it.

Type 4 UR (38); r46c4<>3
Skyscraper, c57; r8c4, r9c8<>9
Finned X-Wing, c49; r5c5<>4
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Sun May 13, 2012 2:17 am    Post subject: Reply with quote

Luke451 wrote:
MUG(34589)r46c24678 ==>r4c8=2

Very nice, but I'm wondering ... How did you convince yourself this was a valid MUG?
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Sun May 13, 2012 5:09 am    Post subject: Reply with quote

ronk wrote:
Luke451 wrote:
MUG(34589)r46c24678 ==>r4c8=2

Very nice, but I'm wondering ... How did you convince yourself this was a valid MUG?

Is this a trick question, Ron? Smile

I took the empirical approach, originally. I pored over the pattern to try to find a reduction that did not result in a BUG-Lite/UR.

When I could not, I did what any doubting dilettante would do. I asked people smarter than me. They were not hard to find.

One accommodating dude by the name of ronk responded,
Quote:
gsf's program shows that placements for this pattern produce only two essentially-different unavoidable sets corresponding to BUG-Lites.
RW:
Quote:
These patterns with two rows in one band are the deadly pattern counterpart to the reverse BUG-lite that I defined a few years ago.

Particularly interesting was David P Bird's examination of externals
Quote:
Considering the external cells that must hold member digits this diagram shows one possible way that (the) pattern can be reduced legitimately to leave ordered BUG-Lite pairs.

All the quotes can be found here, in context.

To answer your question, I did not convince myself. I was convinced. I'm just a dabbler, I leave it to the likes of y'alls to do the heavy lifting Wink
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Sun May 13, 2012 11:41 am    Post subject: Reply with quote

Luke, always nice to have something like that to look at and think about.
From replies, I cannot tell whether it is accepted and proven that this is a MUG.
If so, then I'll have to go back to the drawing board, and think a little better, because I don't see it as such.
Firstly I've converted from the digits in the specific case to abcde, so the starting position is
Code:

     .  .   ab | abcd . ace | cd abe .   

     .  .   ab | abcd . ace | cd abe .   

Assign a to r1c3=>br2c3
Now given the AUR(cd)r12c47 this forces a or b somewhere in r12c4. Then AUR(ab)r12c34 prevents both a+b in r12c4, so there are only two configurations possible : r1c4=b or r2c4=a. Each forces assignment throughout the entire pattern as follows :
Code:

        .  .   a  |b . c | d . e 
        .  .   b  |d . e | c . a

        .  .   a  |d . e | c . b 
        .   .  b  |a . c | d . e

Now assign b to r1c3=>ar2c3
Again, given AUR(cd)r12c47, this forces a or b somewhere in r12c4. Again AUR(ab)r12c34 prevents both a+b in r12c4, so there are only two configurations possible : r1c4=a or r2c4=b. Each forces assignment throughout the entire pattern as follows :
Code:

        .   .  b  |a . c | d . e 
        .   .  a  |d . e | c . b 

        .   .  b  |d . e | c . a 
        .   .  a  |b . c | d . e

Since all possibilties for r1c3 have been examined, we have a total of 4 possibilities : call them respectively 1 2 3 4. Then 1 and 4 are equivalent (if one is solution, so is the other). Equally 2 and 3 are equivalent. But different from 1 and 3.
So unless one of those pairings is invalid, it seems to me that there cannot be MUG. Such would be the case if one of those pairings was an overlay of unavoidables to quote ronk quoting RW in the link which you give, but that does not look the case here, unless I'm in a wood and trees scenario, never to be ruled out.
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Sun May 13, 2012 11:42 am    Post subject: Reply with quote

Luke451 wrote:
ronk wrote:
Luke451 wrote:
MUG(34589)r46c24678 ==>r4c8=2
Very nice, but I'm wondering ... How did you convince yourself this was a valid MUG?
Is this a trick question, Ron? Smile

I asked people ... All the quotes can be found here, in context.

Sorry, not a trick question. I had forgotten all but one highlight of that discussion. Sad Embarassed
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Mon May 14, 2012 12:45 am    Post subject: Reply with quote

aran, are you trying to say I'm wrongly convinced??

Very interesting breakdown of that particular pattern. I got out a pencil and paper and broke it down with consideration of the potential UR. My results were exactly the same as yours.

1 and 4 were mirrors, as were 2 and 3, and the latter is different from the former. I still trying to wrap my head around how it's a legal pattern when either way results in two solutions.

The 4 candidate single band pattern seems to be proven and accepted as a MUG:
Code:
     .  abcd .  | abcd  .  abcd | .  abcd  .
     .    .  .  |   .   .    .  | .   .    .
     .  abcd .  | abcd  .  abcd | .  abcd  .

The question of what makes and proves a MUG continues to be one of the remaining grey areas of sudoku, hence my fascination with them.
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Mon May 14, 2012 6:02 pm    Post subject: Reply with quote

Luke
We're agreed about the results. All that remains is the interpretation.
As I see it :
in a UP setting (MUG BUG UR), ignoring the UP breaking candidate(s) which must exist, there can be no latitude, everything is forced, and the UP candidates are hermetically sealed inside the UP.
Here I don't...yet...see that this is the case because AUR(cd) does not force r1c4, it forces something over r12c4 but there is enough latitude there for non-UP.
At the moment there are four viable solutions.
1 is viable, so is 3 and they are different.
The fact that 1 is viable, and so is 4, and that they are the same...is unfortunate...but I think (for the time being...) irrelevant !

A tricky area though.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Mon May 14, 2012 7:21 pm    Post subject: Reply with quote

aran, I think I heard what I wanted to hear from the replies to my question at Players'.

When ronk said "gsf's program shows that placements for this pattern produce only two essentially-different unavoidable sets corresponding to BUG-Lites," perhaps the program just found the two different sets that you did. Just guessing here.

I took that to mean that the pattern reduced to BUG-Lites and was therefore deadly, but that's not what was said.

Also, though I'm not up on "Reverse Bug-Lites," now I'm wondering if that stategy produces any different results for this pattern. RW seemed to imply that was the case in his quote above.
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Tue May 15, 2012 2:17 am    Post subject: Reply with quote

Luke451 wrote:
Code:

  .     49    .     | 3489  .     345   | 38    459   .
  .     .     .     | .     .     .     | .     .     .
  .     49    .     | 3489  .     345   | 38    459   .
MUG(34589)r46c24678

It is relatively easy to show that this (partially-permeated) prospective MUG can only be reduced to one of the following three:
Code:

 .  49 .  | 89 .  35 | 38 45 .
 .  .  .  | .  .  .  | .  .  .
 .  49 .  | 89 .  35 | 38 45 .


 .  49 .  | 48 .  35 | 38 59 .
 .  .  .  | .  .  .  | .  .  .
 .  49 .  | 48 .  35 | 38 59 .


 .  49 .  | 38 .  45 | 38 59 .
 .  .  .  | .  .  .  | .  .  .
 .  49 .  | 38 .  45 | 38 59 .

By inspection, the first and second are 10-cell BUG-Lites, and the last is an overlay of a UR(38 ) and a 6-cell BUG-Lite. Therefore, the prospective MUG is an actual MUG.

Since the second can be permuted to the first, in this case by merely swapping digits '4' and '9', the two are equivalent, i. e., not essentially different.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Wed May 16, 2012 1:08 am    Post subject: Reply with quote

Gentlemen, thank you for taking the time to parse out this pattern.

Here's what one of my so-called "empirical approaches" looks like.
It's enough to make one's eyes glaze over...


Code:
  .     49    .     | 3489  .     345   | 38    459   .
  .     .     .     | .     .     .     | .     .     .
  .     49    .     | 3489  .     345   | 38    459   .


r13c4 can contain one of six possible combinations:

*34 *38 *39 *48 *49 *89

Code:
  .     49    .     |*34  .     5   | 38    459  .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*34  .     5   | 38    459  .

Two 5s/no solution c6


Code:
  .     49    .     |*38  .     45  | 38    59   .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*38  .     45  | 38    59   .

UR plus BUG-Lite


Code:
  .     49    .     |*39  .    45   | 38    5    .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*39  .    45   | 38    5    .

Two 5s/no solution c8 (or suffice it to say, there's conjugate 8s here this particular grid)


Code:
  .     49    .     |*48  .     35  | 38    59   .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*48  .     35  | 38    59   .

BUG-Lite


Code:
  .     49    .     |*49  .     35  | 38    5    .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*49  .     35  | 38    5    .

Two 5s/no solution c8


Code:
  .     49    .     |*89  .     35  | 38    45   .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*89  .     35  | 38    45   .

BUG-Lite


These results show a deadly pattern, a combination of deadly patterns,
or no solution. The deadly patterns and overlays correspond to ronk's
findings above.
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Wed May 16, 2012 1:29 pm    Post subject: Reply with quote

Luke451 wrote:
Code:
  .     49    .     |*39  .    45   | 38    5    .
  .     .     .     | .   .     .   | .     .    .
  .     49    .     |*39  .    45   | 38    5    .

Two 5s/no solution c8 (or suffice it to say, there's conjugate 8s here this particular grid)

For a "no solution" result, there is no point in having mostly bivalues. In this case, using (3459) naked quads is direct and effective.
Code:
  .     49    .     |*39  .    345  |  8    459  .
  .     .     .     | .   .    .    | .     .    .
  .     49    .     |*39  .    345  |  8    459  .

Two 8s/no solution c7

My method started with digits 4 and 9 ultimately needing to be placed one each in the middle mini-rows of boxes 2 and 3 (5 and 6 of the actual puzzle). It's not necessarily a better method, just different.
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aran



Joined: 19 Apr 2010
Posts: 70

PostPosted: Thu May 17, 2012 11:10 am    Post subject: Reply with quote

Luke
Just back from that parallel MUG-free universe.
Yes that MUG of yours was a very nice find Very Happy

Having had to think about it, here are some thoughts (already expressed by many others, notably RW, all I'm merely doing is re-discovering for myself and saying things in my own way) :
- let there be a locked set of N candidates in N cells in a row
- in another row on the same floor, let there be the same N candidates locked in the same N relative cells.
For shorthand call that configuration the N-pattern.
Then N-pattern is MUG/impossible.
Whether N be 2 or 9, N-pattern => MUG/impossible
Simple explanation :
let S be any solution to those 2N cells
then W is also a solution, where W= xx the relative partners (xx having no external effect on columns, rows, boxes).

Concerning cases beyond N=4.
N=9 : => absence of givens in such a configuration is impossible =>in a sudoku with a unique solution, there cannot be two rows in same floor without any givens.
N=8 : impossible =>implies same remaining candidate occurs in both relative cells
N=7,6,5 : there must be a reverse MUG/impossible pattern in the "other" cells.
This means that one can look for this reverse pattern as an alternative to examination of the other.
In particular it means that this reverse pattern can include givens as well as assigned. This notion always comes as a surprise because of the tendency to think of givens as barriers to uniqueness (eg UR).
I think this could be formulated as :
if all the givens and assigned would generate an N-pattern, then those givens and assigneds cannot exist.

To take an example for N=5 ie your example
Code:

 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | *1    49   *25    |3489   *6     345  |38     59+2  *7    |
 | 8     3     25    | 149   479   1457  | 59    6     24    |
 | *7    49   *6     |3489   *2     345  |38     59    *1    |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134   47    1347  | 15    2457  8     |
 | 3     127   8     | 149   5     6     | 19    2479  24    |
 | 5     17    4     | 2     789   178   | 6     79    3     |
 *-----------------------------------------------------------*


Here in r46c1359 we have a 1267 set-up which would generate a 34589 N-pattern.
That is, if r46c1359 consist only of 1267 regardless of which are givens and which are assigned (that being the key point), then an N-pattern would result in r46c24678
Hence r46c1369=1267 being impossible =><2>r4c3
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Fri May 18, 2012 4:33 am    Post subject: Reply with quote

I looked into the Reverse BUG-Lite perspective. This may be the way to go when the MUG gets big Idea
Code:
 *-----------------------------------------------------------*
 | 9     8     7     | 5     1     2     | 4     3     6     |
 | 4     6     1     | 7     3     9     | 2     8     5     |
 | 2     5     3     | 6     48    48    | 7     1     9     |
 |-------------------+-------------------+-------------------|
 | 1     49   *25    | 3489 *6     345   | 38    4592  7     |
 | 8     3     25    | 149   479   1457  | 59    6     24    |
 | 7     49   *6     | 3489 *2     345   | 38    459   1     |
 |-------------------+-------------------+-------------------|
 | 6     127   9     | 134   47    1347  | 15    2457  8     |
 | 3     127   8     | 149   5     6     | 19    2479  24    |
 | 5     17    4     | 2     789   178   | 6     79    3     |
 *-----------------------------------------------------------*

Now I'm wondering if just these four cells are enough to make the Reverse Bug-Lite elimination of r4c3<>2. This grid is a little different than most Rev B-L in that at this point the (6) value is solved for the whole puzzle.
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