Everything about Sudoku that doesn't fit in one of the other sections
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!!)
Mike Barker

Posts: 458
Joined: 22 January 2006

### Another try at U-Loops

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 99 . . | 4 . 8 | . . 5. . 8 | . . . | 3 . .---------------------. 8 . | 5 2 7 | . 3 .4 . . | 3 . 6 | . . 7. 3 . | 8 4 9 | . 5 .---------------------. . 2 | . . . | 9 . .8 . . | 9 . 5 | . . 21 9 . | . 8 . | . 7 3`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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 .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

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.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

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
RW
2010 Supporter

Posts: 1000
Joined: 16 March 2006

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.
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

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

tarek

tarek

Posts: 3416
Joined: 05 January 2006

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
`5.47.61.361.439..53..5.1..6..6.1435775369..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.
Eioru

Posts: 182
Joined: 16 August 2006

### Bug+2

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 | . . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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.
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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]`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

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

tarek

tarek

Posts: 3416
Joined: 05 January 2006

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.
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

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