The New Sudoku Players' Forum

[Dogguk]

Just don't know what to do without guessing from here...


1 . 9 | . . . | 7 . .
. 2 7 | . . . | 5 . .
6 4 5 |3 8 7| 9 2 1
-------------------------
. 7 8 | . . . | 6 9 .
. . 1 | 6 . 9| 2 . 8
9 6 2| . . . | 1 4 .
-------------------------
- - 6 |4 2 5 |3 - 9
2 - 3 | - - - | 4 6 -
- - 4 | - - - | 8 - 2

[tarek]

It would always help if you would post a Pencilmark grid, this would show us exactly where you've reached in your chain of thoughts.

Here I'm guessing you've reached this point where you will need an advanced technique, one suggestion would be:

Code: Select all

*--------------------------------------------------------*
| 1     38    9    | 25    456   246  | 7     38    46   |
| 38    2     7    | 19    1469  146  | 5     38    46   |
| 6     4     5    | 3     8     7    | 9     2     1    |
|------------------+------------------+------------------|
|#345   7     8    | 125   1345  1234 | 6     9     35   |
|*345  -35    1    | 6     3457  9    | 2    *57    8    |
| 9     6     2    | 578   357   38   | 1     4     357  |
|------------------+------------------+------------------|
| 78    18    6    | 4     2     5    | 3     17    9    |
| 2     159   3    | 1789  179   18   | 4     6     57   |
|*57    159   4    | 179   36    36   | 8    *157   2    |
*--------------------------------------------------------*
Eliminating 5 From r5c2 (Finned XWing in Columns 18 with 1 fin in Box 4)

The full name of this fish is non-sashimi finned basic x-wing.

tarek

[Bigtone53]

There is much discussion on what constitues guessing but given Tarek's pencilmarks, what are the consequences of Row 8 column 9 being a 5? It may have an advanced name but the consequences are straightforward.

[Dogguk]

You may have to explain, because I don't see any negative consequences to adding a 5 in r8c9. I had the same detailed pencil marks as Tarak btw. except for the -3 he has, I can't get to that conclusion...

Thanks tho, you guys really have this stuff down.

[daj95376]

You may have to explain, because I don't see any negative consequences to adding a 5 in r8c9. I had the same detailed pencil marks as Tarak btw. except for the -3 he has, I can't get to that conclusion...

Thanks tho, you guys really have this stuff down.

tarek is among a number of people who place a minus sign '-' in front of a list of candidates where an elimination occurs. You must also take note that he is talking about an elimination for the candidate 5.

I would have changed '-35' to '3-5' to show all eliminations grouped at the end.

[tarek]

I would have changed '-35' to '3-5' to show all eliminations grouped at the end.

I agree that it would be visually more understandable to do it that way, Dogguk was the 1st to point out that writing down the elimination under the grid wasn't enough....

I always write the eliminations the way I do because of issues arising when trying to explain batch eliminations & multiple different candidate eliminations.

I guess for a simple x-cycle eliminations it is better to write it '3-5'

here are some other more complex alterrnatives showing that same elimination

Code: Select all

*--------------------------------------------------------*
| 1     38    9    | 25    456   246  | 7     38    46   |
| 38    2     7    | 19    1469  146  | 5     38    46   |
| 6     4     5    | 3     8     7    | 9     2     1    |
|------------------+------------------+------------------|
| 345   7     8    | 125   1345  1234 | 6     9     35   |
| 345   3-5   1    | 6     3457  9    | 2    #57    8    |
| 9     6     2    | 578   357   38   | 1     4     357  |
|------------------+------------------+------------------|
| 78    18    6    | 4     2     5    | 3     17    9    |
| 2    #159   3    | 1789  179   18   | 4     6     57   |
|*57   *159   4    | 179   36    36   | 8    *157   2    |
*--------------------------------------------------------*
Sashimi Finned Franken X-wing c8b7/r9b4 fins=[r5c8][r8c2] --> [r5c2]<>5

*--------------------------------------------------------*
| 1     38    9    | 25    456   246  | 7     38    46   |
| 38    2     7    | 19    1469  146  | 5     38    46   |
| 6     4     5    | 3     8     7    | 9     2     1    |
|------------------+------------------+------------------|
| 345   7     8    | 125   1345  1234 | 6     9    *35   |
| 345   3-5   1    | 6     3457  9    | 2    #57    8    |
| 9     6     2    | 578   357   38   | 1     4    *357  |
|------------------+------------------+------------------|
| 78    18    6    | 4     2     5    | 3     17    9    |
| 2    #159   3    | 1789  179   18   | 4     6    *57   |
| 57    159   4    | 179   36    36   | 8     157   2    |
*--------------------------------------------------------*
Sashimi Finned Franken X-wing r8b6/c9b4 fins=[r5c8][r8c2] --> [r5c2]<>5

[Bigtone53]

There is much discussion on what constitues guessing but given Tarek's pencilmarks, what are the consequences of Row 8 column 9 being a 5?

The technique is often called colouring (or coloring for our American friends ), Here the colouring is in 5s

r8c9 is either a 5 or it isn't, but we do not know which. Colour it say blue
As the only other 5 possibility in box 9, r9c8 is the opposite of r8c9. Colour r9c8 green
As the only other 5 possibility in c8, colour r5c8 blue

Meanwhile,
As the only other 5 possibility in r8, colour r8c2 green

You now have r5c2 'seeing' both a green and a blue. As either all the green squares or all the blue squares are 5s, r5c2 is not a 5.

[eleven]

The finned x-wing is also a grouped skyscraper.
What Bigtone53 described, is a kite, There is another kite for 7 (row 5, col 9, r8c5 != 7).
There is a y-wing 57 (r5c8, r9c1) with link 7 in row 7, r5c1 != 5, r9c8 != 5.
A y-wing 57 (r8c9, r9c1) with link 7 in row 7, r8c2 != 5, r9c8 != 5.
A y-wing 35 with link 5 in row 8, r4c1 != 3.

[Dogguk]

Thanks Big, I "get it" now. I never worked with coloring, I love it!

[Cec]

Thanks Big, I "get it" now. I never worked with coloring, I love it!

I'm pleased Dogguk "fell in love" with Bigtone's clear explanation of the colouring technique - I also find colouring easier to understand than alternative advanced techniques.

Dogguk, you might like to read up more on colouring which is mentioned with other basic solving techniques in the following link: http://www.angusj.com/sudoku/hints.php

Cec

[Dogguk]

I'm trying so hard to get the "Swordfish" but it just ain't clicking. I'm hopin Big or someone can dumb that one down for me..

[Bigtone53]

I'm trying so hard to get the "Swordfish" but it just ain't clicking

Dogguk,

The Swordfish is X-wing's big brother (and there are yet bigger brothers) so I suggest that you are rock solid on X-wings before stepping up a level.

I suspect that it is simplest to explain swordfishes through diagrams but I am no good at getting my diagrams to look nice . I am sure that the experts can explain (and illustrate) much better than I can but I will give it a go if you are still unsure.

Here, from Simple Sudoku, is a grid that is most simply solved using the swordfish technique. Hopefully, it will help knowing that there is one there.

Code: Select all

 *-----------*
 |..2|..5|37.|
 |7..|9..|..8|
 |61.|...|...|
 |---+---+---|
 |..8|.1.|...|
 |.7.|.3.|.5.|
 |...|.2.|4..|
 |---+---+---|
 |...|...|.32|
 |5..|..6|..7|
 |.41|7..|9..|
 *-----------*

 


[Cec]

Alas, I tried, but unable to produce those preferred "screenshot" grids with coloured cells to best explain Bigtone's above Swordfish example. So here's my explanation after reading up on other threads. Comments are welcome because understanding this technique is new to me also.

A Sword-Fish pattern is formed by either of the following:

(a) three rows each containing no more than three cells with a specific candidate value sharing the same columns OR

(b) three columns each containing no more than three cells with a specific candidate value sharing the same rows.

These cells form a pattern which contain the only possible locations for the candidates in these three rows and columns. Whilst we do not know which cells, that make up the Sword-Fish pattern, must only contain that candidate, we do know that cells outside the Sword-Fish that share the same columns cannot contain that same candidate. After basic eliminations Bigtone's above puzzle reaches this position...

Code: Select all

 *-----------------------------------------------------------*
 | 489   89    2     | 1     46    5     | 3     7     469   |
 | 7     35    345   | 9     46   *23    |*256   1     8     |
 | 6     1     3459  | 23    7     8     |#25    29    459   |
 |-------------------+-------------------+-------------------|
 |#2349  2359  8     | 56    1     49    | 7     269   369   |
 | 1*249 7     469   | 68    3     49    |*268   5     169   |
 | 139   359   3569  | 568   2     7     | 4     689   1369  |
 |-------------------+-------------------+-------------------|
 | 89    6     7     | 4     589   1     | 58    3     2     |
 | 5     2389  39    | 23    89    6     | 1     4     7     |
 |*23    4     1     | 7     58   *23    | 9     68    56    |
 *-----------------------------------------------------------*


It will be seen that candidate 2 (marked with an asterisk) appears no more than three times in each of the three rows 2,5 and 9 and share the same three columns 1,6 and 7. Although we cannot yet determine which of the cells marked * must contain candidate 2 we can exclude any other candidate 2's outside the Swordfish which shares the same column. Therefore, candidate 2's can be excluded from r4c1 and r3c7 (shown thus #)which leaves only candidate 5 in r3c7 and thus solving the remaining puzzle by basic eliminations.

Cec

[daj95376]

I should direct you to any number of excellent sources on the topic of basic Fish, but ...

Sometimes a visual helps. The first grid is our old friend the X-Wing with 2 candidates in 2 rows that are restricted to 2 columns. The eliminations (*) occur in the restricted columns.

Code: Select all

 +-----------------------------------+
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |  /  X  /  |  /  /  /  |  /  X  /  |
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  .  .  |  .  *  .  |
 |  /  X  /  |  /  /  /  |  /  X  /  |
 |  .  *  .  |  .  .  .  |  .  *  .  |
 +-----------------------------------+


Now, we extend the grid to 3 rows that are restricted to 3 columns. This is a Swordfish where each row contains 2 candidates.

Code: Select all

 +-----------------------------------+
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  X  /  |  /  /  /  |  /  X  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  X  /  |  /  X  /  |  /  /  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  /  /  |  /  X  /  |  /  X  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 +-----------------------------------+


Now is where the fun begins. It's perfectly okay to add another candidate to any (or all) of the 3 rows -- as long as you don't change the number of columns. So, this example is also a Swordfish.

Code: Select all

 +-----------------------------------+
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  X  /  |  /  X  /  |  /  X  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  X  /  |  /  X  /  |  /  X  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |-----------+-----------+-----------|
 |  .  *  .  |  .  *  .  |  .  *  .  |
 |  /  X  /  |  /  X  /  |  /  X  /  |
 |  .  *  .  |  .  *  .  |  .  *  .  |
 +-----------------------------------+


Now, because more complex Fish exist, the complete name for my two examples is non-sashimi unfinned basic Swordfish r258\c258. Only tarek would ever call it this!

Note #1: As in the X-Wing, the whole thing could have been expressed as candidates in columns that were restricted to rows. Then the eliminations would be in the restricted rows.

Note #2: Do not confuse my use of (*) for elimination cells with Cec's use of (*) to mark (X) cells. Unfortunately, two different display formats use the same symbol to mean different things. Also note that it would have been better if Cec had used (-) instead of (#) for the elimination cells because convention reserves that symbol to mean something else.

Final Note: My grids are not based on the puzzle and PM posted above.

[eleven]

Try this: http://forum.enjoysudoku.com/viewtopic.php?p=52168#p52168