Is this the "Best Ever Swordfish Sudoku"?

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Is this the "Best Ever Swordfish Sudoku"?

Postby tso » Thu Jul 06, 2006 3:58 pm

Code: Select all
+-------+-------+-------+
| 9 . . | 4 . . | 7 . . |
| . 6 . | . 3 . | . 5 . |
| . . 1 | . . 8 | . . 4 |
+-------+-------+-------+
| 2 . . | 8 . . | 1 . . |
| . 3 . | . 4 . | . 7 . |
| . . 7 | . . 9 | . . 5 |
+-------+-------+-------+
| 5 . . | 6 . . | 2 . . |
| . 2 . | . 8 . | . 9 . |
| . . 6 | . . 1 | . . 3 |
+-------+-------+-------+


+-------------------+-------------------+-------------------+
| 9     58    2358  | 4     1256  256   | 7     12368 1268  |
| 478   6     248   | 1279  3     27    | 89    5     1289  |
| 37    57    1     | 2579  25679 8     | 369   236   4     |
+-------------------+-------------------+-------------------+
| 2     459   459   | 8     567   3567  | 1     346   69    |
| 168   3     589   | 125   4     256   | 689   7     2689  |
| 1468  148   7     | 123   126   9     | 3468  23468 5     |
+-------------------+-------------------+-------------------+
| 5     14789 3489  | 6     79    347   | 2     148   178   |
| 1347  2     34    | 357   8     3457  | 456   9     167   |
| 478   4789  6     | 2579  2579  1     | 458   48    3     |
+-------------------+-------------------+-------------------+



Is this the best Swordfish puzzle ever?


Count them -- Six Swordfish existing in the opening position -- and no other simpler moves are possible! No naked or hidden singles, no naked or hidden sets of any size, no locked candidates, no x-wings, xy-wings, no Unique Rectangles or loops, no xy-type forcing chains of any size.

SF 1s in rows: r2c49-r5c14-r8c19
SF 1s in columns: r67c2-r16c5-r17c8
Both make the same 4 exclusions: r1c9, r6c14, r7c9 <>1

SF 2s in rows: r3c458-r6c458-r9c45
SF 2s in columns: r12c3-r125c6-r125c9 [EDIT -- corrected typo]
Both make the same 4 exclusions: r1c58, r2c4, r5c4 <>2

SF 3s in rows: r1c38-r4c68-r7c36
SF 3s in columns: r38c1-r68c4-r36c7
Both make the same 4 exclusions: r3c8, r6c8, r8c36 <>3


A methodical solver is likely to find one of the swordfish in 1s, then in 2s, then in 3s. However, it is both sufficient and necessary to make the exclusion r8c3<>3 to move the puzzle into an "all singles" state.


The exclusion r8c3<>3 can also be made by (Simple Sudoku-Style) Multiple Colors on 3s:

Code: Select all
+-------------------+-------------------+-------------------+
| 9     58   +2358  | 4     1256  256   | 7    -12368 1268  |
| 478   6     248   | 1279  3     27    | 89    5     1289  |
|-37    57    1     | 2579  25679 8     | 369   236   4     |
+-------------------+-------------------+-------------------+
| 2     459   459   | 8     567  x3567  | 1    o346   69    |
| 168   3     589   | 125   4     256   | 689   7     2689  |
| 1468  148   7     |o123   126   9     | 3468  23468 5     |
+-------------------+-------------------+-------------------+
| 5     14789 3489  | 6     79    347   | 2     148   178   |
|+1347  2    *34    |x357   8     3457  | 456   9     167   |
| 478   4789  6     | 2579  2579  1     | 458   48    3     |
+-------------------+-------------------+-------------------+


If the cells marked "+" are true (equal to 3), then the cell marked "*" does not equal 3.
If the cells makred "+" are false, then "-" are true, "o" are false and "x" are true -- and "*" does not equal 3.



This exclusion can also be made by Nishio. Most rate this tactic as more advanced than Swordfish, however, die-hard pen+paper solvers who use Nishio regularly *might* solve the puzzle without using pencil marks by noticing that if r8c3=3 the rest of the 3's cannot be placed.
Last edited by tso on Wed Jul 26, 2006 7:40 pm, edited 1 time in total.
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Postby algernon » Thu Jul 13, 2006 12:43 pm

This is very beauty!
Nothing more to say.
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Postby Darkozin » Thu Jul 13, 2006 8:16 pm

Hi Tso

What is "Swordfish Sudoku." How is it different from regular Sudoku?

-Darkozin-
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error in row markings?

Postby fontenots » Wed Jul 26, 2006 7:08 pm

Hi, I am new to the forums and appreciate finding this site! I am working on spotting swordfish and some of the advanced pencil/paper techniques. This example is very good! Thank you.

I believe I am getting a hold of what to spot, but is there an error in the labeling of the S2?
Posted is:
SF 2s in columns: r23c3-r235c6-r235c9

There is a "1" filled in r3c3. Should S2 be:
r12c3-r125c6-r125c9 ?

Thank you for the example. I kept making many mistakes thinking that I discovered one in a puzzle, only to discover I jumped the gun. The "only in the row/column" thing is what I am trying now to wrap my brain around.
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Joined: 26 July 2006

Re: error in row markings?

Postby tso » Wed Jul 26, 2006 11:41 pm

fontenots wrote:... is there an error in the labeling of the S2?
Posted is:
SF 2s in columns: r23c3-r235c6-r235c9

There is a "1" filled in r3c3. Should S2 be:
r12c3-r125c6-r125c9 ?


You are correct. I've corrected this mistake in the original post.
tso
 
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