The Effortless Extremes thread

Everything about Sudoku that doesn't fit in one of the other sections

Postby Mike Barker » Mon Oct 09, 2006 9:45 pm

One explanation for the eliminations is overlapping nice loops using bivalues/ALS:
r3c6-a-r3c3-c-r2c2-b-r2c5|r3c6~c~ => r1c4<>c
r3c6-c-r3c3-a-r1c1-b-r1c4|r3c6~a~ => r2c5<>a
where the starting ALS/bivalue=r3c6 overlaps the ending ALS=r2c5|r3c6 or r1c4|r3c6
Code: Select all
ab .  .  |*abc .   .
.  bc .  | .  #abc .
.  .  ac | .   .   ac


Also the link to a grouped strong link elimination is here and is summarized here. By-the-by I refer to it as a UR+2rd after its creator (2 diagonal non-bivalue cells, invented by RW!!)
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Another try at U-Loops

Postby wapati » Wed Oct 11, 2006 5:53 am

Here is an "easy" U-Loop type 2.

SE tells me so. I do see the pattern, I'd have a hard time finding it myself.:(

Code: Select all
2 4 . | . 5 . | . 8 9
9 . . | 4 . 8 | . . 5
. . 8 | . . . | 3 . .
---------------------
. 8 . | 5 2 7 | . 3 .
4 . . | 3 . 6 | . . 7
. 3 . | 8 4 9 | . 5 .
---------------------
. . 2 | . . . | 9 . .
8 . . | 9 . 5 | . . 2
1 9 . | . 8 . | . 7 3
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Postby wapati » Wed Oct 11, 2006 6:03 am

Here is a BUG+3, all the action is in the same 9X9.

Code: Select all
. 6 . | 2 . 4 | . 8 .
. . 3 | 5 . 8 | 6 . .
. . . | 6 . 1 | . . .
---------------------
. 5 . | . . . | . 4 .
6 . 1 | . 4 . | 3 . 2
. . 4 | . . . | 1 . .
---------------------
7 . . | 3 6 9 | . . 8
. . . | . . . | . . .
. 8 6 | . . . | 5 7 .
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Postby Carcul » Wed Oct 11, 2006 8:50 am

Wapati wrote:Here is an "easy" U-Loop type 2.


I don't see any simple Unique Loop. Here's what I see:

Code: Select all
 *---------------------------------------------------*
 | 2     4     67  | 167   5     3  | 167   8     9  |
 | 9     167   3   | 4     67    8  | 167   2     5  |
 | 5     167   8   | 1267  9     12 | 3     146   14 |
 |-----------------+----------------+----------------|
 | 6     8     9   | 5     2     7  | 14    3     14 |
 | 4     2     5   | 3     1     6  | 8     9     7  |
 | 7     3     1   | 8     4     9  | 2     5     6  |
 |-----------------+----------------+----------------|
 | 3     5     2   | 167   67    14 | 9     46    8  |
 | 8     67    467 | 9     3     5  | 146   146   2  |
 | 1     9     46  | 26    8     24 | 5     7     3  |
 *---------------------------------------------------*

Note the Unique Pattern in cells r3c89/r4c79/r8c78. So, r7c8 cannot be "6", otherwise the puzzle would have more than one solution.

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Postby Carcul » Wed Oct 11, 2006 9:20 am

Code: Select all
 *------------------------------------------*
 | 15   6    9 | 2    3    4 | 7    8    15 |
 | 124  147  3 | 5    79   8 | 6    29   14 |
 | 245  47   8 | 6    79   1 | 29   3    45 |
 |-------------+-------------+--------------|
 | 3    5    7 | 1    2    6 | 8    4    9  |
 | 6    9    1 | 8    4    7 | 3    5    2  |
 | 8    2    4 | 9    5    3 | 1    6    7  |
 |-------------+-------------+--------------|
 | 7    14   5 | 3    6    9 | 24   12   8  |
 | 14   3    2 | 7    8    5 | 49   19   6  |
 | 9    8    6 | 4    1    2 | 5    7    3  |
 *------------------------------------------*

r2c1=2 or r2c2=7. But:

[r2c1]=2|7=[r2c2]=1=[r7c2]-1-[r7c8]-2-[r2c8]=2=[r2c1].

So r2c1=2.

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Postby RW » Wed Oct 11, 2006 1:56 pm

carcul wrote:I don't see any simple Unique Loop. Here's what I see:

Not that I'm an expert on SE terminology, but I think what you see is a simple uniqe loop... I'll add the puzzle to the BUG-lites.

Then the BUG+3 puzzle:

Code: Select all
 *------------------------------------------*
 | 15   6    9 | 2    3    4 | 7    8    15 |
 | 24+1 17+4 3 | 5    79   8 | 6    29   14 |
 | 25+4 47   8 | 6    79   1 | 29   3    45 |
 |-------------+-------------+--------------|
 | 3    5    7 | 1    2    6 | 8    4    9  |
 | 6    9    1 | 8    4    7 | 3    5    2  |
 | 8    2    4 | 9    5    3 | 1    6    7  |
 |-------------+-------------+--------------|
 | 7    14   5 | 3    6    9 | 24   12   8  |
 | 14   3    2 | 7    8    5 | 49   19   6  |
 | 9    8    6 | 4    1    2 | 5    7    3  |
 *------------------------------------------*


I'm not really sure what to do with this one... The immediate implication, that doesn't involve anything but the three non-bivalue cells, is r2c1<>4 (same elimination can be done by XYZ-wing) - which solves the puzzle together with a XY-wing. However, as it still requires an XY-wing it cannot qualify for the list. If you have an alternative solution that uses the BUG+3 to solve the puzzle in one step, a solution that is simple enough to beat the very obvious two step solution I gave, then please post it.

Mike Barker wrote:By-the-by I refer to it as a UR+2rd after its creator

Nice, I didn't know that I had a technique named after me. Always wondered what those letters in your UR definitions stand for.

RW
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Postby wapati » Wed Oct 11, 2006 5:15 pm

RW wrote:If you have an alternative solution that uses the BUG+3 to solve the puzzle in one step, a solution that is simple enough to beat the very obvious two step solution I gave, then please post it.


I have:

Code: Select all
 *------------------------------------------*
 | 15   6    9 | 2    3    4 | 7    8    15 |
 | 12+4 17+4 3 | 5    79   8 | 6    29   14 |
 | 25+4 -47  8 | 6    79   1 | 29   3    45 |
 |-------------+-------------+--------------|
 | 3    5    7 | 1    2    6 | 8    4    9  |
 | 6    9    1 | 8    4    7 | 3    5    2  |
 | 8    2    4 | 9    5    3 | 1    6    7  |
 |-------------+-------------+--------------|
 | 7    14   5 | 3    6    9 | 24   12   8  |
 | 14   3    2 | 7    8    5 | 49   19   6  |
 | 9    8    6 | 4    1    2 | 5    7    3  |
 *------------------------------------------*


R3C2 cannot be 4, must be 7.
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Postby ronk » Wed Oct 11, 2006 5:42 pm

wapati, the non-BUG candidate in r2c1 is '1' not '4'. You can get to your r3c2<>4 exclusion in one step ... but it requires a rather long chain.
Code: Select all
 15   6    9 | 2    3    4 | 7    8    15
 24+1 17+4 3 | 5    79   8 | 6   *29   14
 25+4 -47  8 | 6   *79   1 |*29   3    45
-------------+-------------+--------------
 3    5    7 | 1    2    6 | 8    4    9 
 6    9    1 | 8    4    7 | 3    5    2 
 8    2    4 | 9    5    3 | 1    6    7 
-------------+-------------+--------------
 7    14   5 | 3    6    9 | 24   12   8 
*14   3    2 | 7    8    5 | 49  *19   6 
 9    8    6 | 4    1    2 | 5    7    3

r2c2-4-r3c2,
r3c1-4-r3c2,
r2c1-1-r8c1=1=r8c8=9=r2c8=2=r3c7=9=r3c5=7=r3c2, implies r3c2<>4
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Postby tarek » Thu Oct 12, 2006 2:35 am

Consider this rare Untouchable puzzle that I came across while generating puzzles for the hardest sudokus:
Code: Select all
 . . 4 | . . 6 | . . . 
 . 1 . | . 3 . | . . . 
 3 . . | 5 . . | . . . 
-------+-------+------
 . . 6 | . . 4 | . . 7 
 . 5 . | . 9 . | . 1 . 
 1 . . | 3 . . | 6 . . 
-------+-------+------
 . . . | . . 7 | . . 8 
 . . . | . 4 . | . 3 . 
 . . . | 1 . . | 5 . .
004006000010030000300500000006004007050090010100300600000007008000040030000100500

after some straight forward moves:
Code: Select all
*-----------------------------------------------------------------*
| 5      289    4     | 7      28     6     | 1      289    3     |
| 6      1      278   | 4      3      9     | 28     278    5     |
| 3      2789  *2789  | 5      28     1     |*2489   24789  6     |
|---------------------+---------------------+---------------------|
| 289    289    6     | 28     1      4     | 3      5      7     |
| 7      5      3     | 6      9      28    | 248    1      24    |
| 1      4      28    | 3      7      5     | 6      289    29    |
|---------------------+---------------------+---------------------|
| 249    3      1     | 29     5      7     |#249    6      8     |
| 29     6      5     | 289    4      28    | 7      3      1     |
| 2489   2789  *2789  | 1      6      3     |*5     -249   -249   |
*-----------------------------------------------------------------*
Eliminating 9 From r9c89 (Finned XWing in Columns 37 with 1 fin in Box 9)

Solving the puzzle.......

Now, As this is a Sashimi variation, the 2 strong links would make Somebody call it a Skyscraper or even a turbot fish........

Some form of colouring would achive the same result.

The Pond has more fish to offer:D

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Postby Eioru » Thu Oct 12, 2006 3:13 am

tarek wrote:
Code: Select all
 . . 4 | . . 6 | . . . 
 . 1 . | . 3 . | . . . 
 3 . . | 5 . . | . . . 
-------+-------+------
 . . 6 | . . 4 | . . 7 
 . 5 . | . 9 . | . 1 . 
 1 . . | 3 . . | 6 . . 
-------+-------+------
 . . . | . . 7 | . . 8 
 . . . | . 4 . | . 3 . 
 . . . | 1 . . | 5 . .



Methods:
59 x Hidden Single 1 x Direct Hidden Pair 2 x Pointing 3 x Turbot Fish

(1) use Hidden Single 12 times
Code: Select all
..47.6...
.1.439...
3..5.1...
..6.14.57
.5.69..1.
1..3756..
....57..8
....4..3.
...1635..


There is a Direct Hidden Pair of (1,3) at R1C7 and R1C9

(2)Then Still use Single and 16 times
Code: Select all
5.47.61.3
61.439..5
3..5.1..6
..6.14357
75369..1.
14.3756..
.31.57.68
.65.4.731
...1635..


2 Pointing => cancel 9 at R6C3 , cancel 8 at R8C1
Then
a Turbot fish : cancel 9 at R7C1 ( R9C3-R3C3-R3C7-R7C7 )
a Turbot fish : cancel 9 at R9C8 ( R9C3-R3C3-R3C7-R7C7 )
a Turbot fish : cancel 9 at R9C9 ( R9C3-R3C3-R3C7-R7C7 )

Final there are 31 Hidden Singles.
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Bug+2

Postby wapati » Thu Oct 12, 2006 4:17 am

Here is a nice BUG+2.

Code: Select all
. . . | . . . | 4 . 3
. 7 . | . . . | 5 8 .
. . . | . . 2 | . 6 1
---------------------
. . . | . 5 . | . 9 .
. . . | 1 . 7 | . . .
. . 6 | . 4 . | 1 . 5
---------------------
8 6 . | . . 3 | . 5 .
. 3 7 | 8 . . | 9 . .
9 . 4 | . . 6 | . . .
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Postby wapati » Thu Oct 12, 2006 4:34 am

ronk wrote:wapati, the non-BUG candidate in r2c1 is '1' not '4'.


I can accept that 1 is a BUG candidate in r2c1, why is "4" not a valid candidate?

Further, if 4 isn't a bug candidate in r2c1 then either r2c1=1 or 4 is needed by the other bugs.
That means r2c1 cannot be 4. Thus BUG+3 forces a BUG+2 which solves.

What troubles me is that BUG might suggest that BUGwise r2c1 is +14.
I don't see a great way to solve using that info.
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Postby daj95376 » Thu Oct 12, 2006 6:52 am

tarek wrote:Consider this rare Untouchable puzzle that I came across while generating puzzles for the hardest sudokus:
Code: Select all
 . . 4 | . . 6 | . . . 
 . 1 . | . 3 . | . . . 
 3 . . | 5 . . | . . . 
-------+-------+------
 . . 6 | . . 4 | . . 7 
 . 5 . | . 9 . | . 1 . 
 1 . . | 3 . . | 6 . . 
-------+-------+------
 . . . | . . 7 | . . 8 
 . . . | . 4 . | . 3 . 
 . . . | 1 . . | 5 . .
004006000010030000300500000006004007050090010100300600000007008000040030000100500

Tarek, you had the right eliminations, but don't need a Sashimi finned X-Wing.

Code: Select all
# after Singles, Naked Triple, Singles, and (2x) Locked Candidates (1)

# Finned X-Wing on <8> in [r26c38] => [r13c8]<>8
# (not needed ... just included as a FYI)
 *--------------------------------------------------------------------*
 | 5      289    4      | 7      28     6      | 1     -289    3      |
 | 6      1     *278    | 4      3      9      |#28    *278    5      |
 | 3      2789   2789   | 5      28     1      | 2489  -24789  6      |
 |----------------------+----------------------+----------------------|
 | 289    289    6      | 28     1      4      | 3      5      7      |
 | 7      5      3      | 6      9      28     | 248    1      24     |
 | 1      4     *28     | 3      7      5      | 6     *289    29     |
 |----------------------+----------------------+----------------------|
 | 249    3      1      | 29     5      7      | 249    6      8      |
 | 29     6      5      | 289    4      28     | 7      3      1      |
 | 2489   2789   2789   | 1      6      3      | 5      249    249    |
 *--------------------------------------------------------------------*

# Finned Squirmbag/Starfish on <9> in [c12347] => [r9c89]<>9
# (Fin: [r1c2]=9 => [r9c3]=9 => [r9c89]<>9)
 *--------------------------------------------------------------------*
 | 5     #289    4      | 7      28     6      | 1      29     3      |
 | 6      1      278    | 4      3      9      | 28     278    5      |
 | 3     *2789  *2789   | 5      28     1      |*2489   2479   6      |
 |----------------------+----------------------+----------------------|
 |*289   *289    6      | 28     1      4      | 3      5      7      |
 | 7      5      3      | 6      9      28     | 248    1      24     |
 | 1      4      28     | 3      7      5      | 6      289    29     |
 |----------------------+----------------------+----------------------|
 |*249    3      1      |*29     5      7      |*249    6      8      |
 |*29     6      5      |*289    4      28     | 7      3      1      |
 |*2489  *2789  *2789   | 1      6      3      | 5     -249   -249    |
 *--------------------------------------------------------------------*

# Followed by Singles to complete solution.

Note:
Code: Select all
r3c7,r6c8,r7c1,r7c4,r8c1,r9c8,r9c9 <> 9     Double Implication Chain on <9> in [r1]
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Postby tarek » Thu Oct 12, 2006 9:51 am

daj95376 wrote:Tarek, you had the right eliminations, but don't need a Sashimi finned X-Wing.

Well, I think it solved it......I must admit that you lost me this time:(
daj95376 wrote:# after Singles, Naked Triple, Singles, and (2x) Locked Candidates
the Naked triple is also a HIDDEN double

daj95376 wrote:# Finned X-Wing on <8> in [r26c38] => [r13c8]<>8
# (not needed ... just included as a FYI)
# Finned Squirmbag/Starfish on <9> in [c12347] => [r9c89]<>9
# (Fin: [r1c2]=9 => [r9c3]=9 => [r9c89]<>9)
I agree that the classic finned x-wing in 8s is not needed, The Finned squirmbag is the alter ego of the finned Xwing I posted......Essentially, There is no larger fish than the finned Jellyfish

Eioru wrote:a Turbot fish : cancel 9 at R7C1 ( R9C3-R3C3-R3C7-R7C7 )
a Turbot fish : cancel 9 at R9C8 ( R9C3-R3C3-R3C7-R7C7 )
a Turbot fish : cancel 9 at R9C9 ( R9C3-R3C3-R3C7-R7C7 )

Fish, Fish & more fish

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Postby ronk » Thu Oct 12, 2006 10:12 am

wapati wrote:I can accept that 1 is a BUG candidate in r2c1, why is "4" not a valid candidate?

Because after the Bug+Nonbug split, candidates in the bivalues -- including the bivalues on the B side -- must appear exactly twice in each row, column, and box.

wapati wrote:Thus BUG+3 forces a BUG+2 which solves.

The BUG+2 certainly seems like the "natural" next step.

wapati wrote:What troubles me is that BUG might suggest that BUGwise r2c1 is +14.
I don't see a great way to solve using that info.

Corollary 4 of the BUG principle ...
Jeff wrote:Corollary 4: Any placement of a candidate which forces a grid into a BUG+1 is a valid move. (example)

... allows us to set r2c1=2 which solves. I'm not sure if that ties to your r2c1=2+14 idea or not.
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