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Brian Regular
Joined: 30 Jan 2007 Posts: 11 Location: Stockholm, Sweden.

Posted: Fri Aug 31, 2007 12:05 pm Post subject: Spotted at last, the rare & elusive ”Blue finned swordfi 


Anyone who regularly does Clueless Explosions, and frequents this forum, must be aware of what I like to call ”blue logic”. That is, solving techniques that depend on the fact that the blue squares in the white puzzles form an extra house. These techniques will not work for a normal sudoku puzzle or a clueless special. One of these, that has already been described in this forum, lets you remove all the white candidates for a number from a row (or column) if all the blue numbers are confined to that row (or column). (By ”blue numbers” I mean the candidates that make up the blue puzzle that we have to solve, and ”white” numbers are the candidates in the other puzzles that are not in blue cells.)
I have long considered posting a description to this forum of the other examples of ”blue logic” I have discovered. I am sure they are not necessary to solve the puzzles, but, if you spot them, they must help to speed up the solution process. Before trying to write a description I thought they should have names. I thought the technique mentioned above could be called the ”White exclusion principle”, since it excludes white candidates. Another could then be called the ”Blue exclusion principle”. Yet another that I often use could be called the ”Blue finned xwing”.
Eureka! If there is such a thing as a ”Blue finned xwing” there must be blue finned swordfish too!
I waited anxiously for the next explosion and kept my eyes pealed watching for this elusive fish while I solved the puzzle No luck. The following week, still no luck. I started doing old explosions from the archive. Still no luck. Finally, a few weeks ago, in explosion number 58 I found not one, but three blue finned swordfish.
I understand sashimi and finned fish. I have not yet understood the descriptions I have read of Mutant, Kracken or Frankenfish. I suspect that my “blue finned” fish may be one of these. If so, I would be grateful if someone could tell me which.
Blue logic:
To view the examples below, I recommend that you start the SudoCue program, chose File – Variant – Center Dot, copy the code for the example and paste it into the program. Then highlight the digit referred to in the example and pretend that the centre dot cells are blue. All the examples are taken from Clueless Explosions and when I wrote these descriptions I was looking at screen dumps from the Clueless Helper that I had saved as bit maps. When I went to upload this document to the forum I discovered that it is not so easy to include images.
White exclusion principle.
While this has been described elsewhere, I describe it again here for completeness. If all the blue candidates for a particular digit occupy the same house, the digit must be in one of the blue cells. Therefore all white candidates for the digit can be eliminated from the house.
Example
Code:  {469} 2 {4679} 3 {1679} 5 {147} 8 {79}
5 {4678} {46789} {46789} {6789} {14679} {1247} {249} 3
{3489} {3478} 1 {4789} 2 {479} 6 {459} {579}
7 {34568} {45689} {24689} {689} {2469} {2345} {234569} 1
{4689} {1468} {4689} 5 {16789} 3 {247} {2469} {2679}
2 {13456} {4569} {4679} {1679} {14679} {3457} {34569} 8
{68} {5678} 3 {267} 4 {267} 9 1 {256}
1 {5678} {25678} {2679} {35679} {2679} {2358} {2356} 4
{46} 9 {2456} 1 {356} 8 {235} 7 {256} 
All the blue candidate twos are in column 8. Therefore you can remove the white candidate two from row 4 column 8.
Blue exclusion principle.
If all the candidates for a particular digit in a house are blue, the blue number must be in that house and all other blue candidates can be eliminated from the white puzzle.
Example
Code:  {17} 9 3 5 {12} 6 {127} 4 8
{1457} {245} {2457} 3 8 9 {1257} {127} 6
{158} {128} 6 {12} 7 4 {125} 9 3
{14678} {178} {479} {124} {12} 5 {14789} 3 {2479}
{14578} {345} {457} 9 6 {78} {12478} {127} {2457}
2 {178} {4579} {14} 3 {78} {14789} 6 {4579}
{47} {27} 1 6 5 3 {2479} 8 {2479}
3 {245} {2457} 8 9 1 6 {27} {247}
9 6 8 7 4 2 3 5 1 
There are no white candidate twos in column 8, so the two must be in one of those blue cells and can be excluded from row 2 column 2 and row 8 column 2
Blue finned xwing.
If all the blue candidates occupy two parallel houses (two rows or two columns) and there exists a strongly linked pair of white candidates in the same houses, all other white candidates can be eliminated from these houses.
Example
Code:  1 9 7 2 {3456} {456} {456} {356} 8
{356} 8 4 1 {3569} 7 {2569} {2356} {23569}
{356} {356} 2 {3469} 8 {4569} 1 7 {34569}
{34569} {13456} {13569} {3469} {123456} {124569} 7 8 {123456}
{34569} 7 {13569} 8 {1234569} {124569} {2456} {12356} {123456}
8 2 {1356} 7 {13456} {1456} {456} 9 {13456}
{45679} {1456} {1569} {469} {1246} 3 8 {1256} {125679}
{4679} {146} {1689} 5 {12469} {124689} 3 {126} {12679}
2 {1356} {135689} {69} 7 {1689} {569} 4 {1569} 
In row one we have a pair of strongly linked white threes. They are in columns 5 and 8. All the blue candidates are also in these columns. In this example there is nothing to eliminate from column 8, but you can eliminate the threes from column 5 rows 4 and 6. If the three in row one is in column 5 you obviously can’t have a three in either of these cells. If it is not, then it has to be in column 8, which means that the blue three has to be in column 5. So you can never have a three in either of these cells.
The blue finned swordfish.
If the blue candidates are distributed across all three columns where you have blue cells and you can find two rows that only contain white candidates in the same columns you can eliminate all other white candidates from those columns. This is also true if you interchange the words row and column in the above statement.
Example 1
Code:  {46} {12456} 7 3 {12456} 8 9 {12456} {146}
{4689} {1245689} {124569} {2456} {124569} {12579} {124568} {1234568} {1346}
3 {1245689} {124569} {2456} {124569} {1259} {124568} {124568} 7
1 {24678} {246} 9 {2678} 3 {4678} {4678} 5
{46789} {2346789} {23469} {2568} {25678} {257} {14678} {1346789} {13469}
5 {36789} {369} 1 {678} 4 {678} {36789} 2
2 {1345679} {134569} {45} {13459} {159} {14567} {145679} 8
{4679} {1345679} {134569} {2458} {1234589} {1259} {124567} {1245679} {1469}
{49} {1459} 8 7 {12459} 6 3 {12459} {149} 
The white candidate fives in rows 1 and 9 are all in the same columns as the blue numbers. The five in row one must be in one of these three columns. Whichever one it occupies will eliminate all other fives in the column leaving two fives in row nine to form a blue finned xwing with the remaining blue numbers. So you can eliminate the candidate fives from row 3 columns 2, 6, and 8, and row 7 columns 2, 6 and 8.
Example 2
Code:  {46} {12456} 7 3 {12456} 8 9 {12456} {146}
{4689} {1245689} {124569} {2456} {124569} u7 {124568} {1234568} {1346}
3 {124689} {124569} {2456} {12469} {1259} {124568} {12468} 7
1 {24678} {246} 9 {2678} 3 {4678} {4678} 5
{46789} {2346789} {23469} {2568} {25678} {25} {14678} {1346789} {13469}
5 {36789} {369} 1 {678} 4 {678} {36789} 2
2 {134679} {134569} {45} {1349} {159} {14567} {14679} 8
{4679} {1345679} {134569} {2458} {1234589} {1259} {124567} {1245679} {1469}
{49} {1459} 8 7 {12459} 6 3 {12459} {149} 
The candidate eights in columns 1 and 4 are all in the same rows as the blue numbers. You can eliminate the eights from column 7 rows 2 and 5. The eight in column 1 has to be in either row 2 or five. If it is in row 2 this eliminates the candidate from row 2 column 7 and the other blue eights from this row. That leaves a blue finned xwing to eliminate the other eight from row 5 column 7. If, on the other hand, the eight in column 1 is in row 5, that immediately eliminates the eight in row 5 column 7 and forces the eight in column 4 into row 8. This means that the blue eight has to be in row 2 and we can never have an eight in row 2 column 7.
Example 3
Code:  {46} {12456} 7 3 {12456} 8 9 {12456} {146}
{4689} {1245689} {124569} {2456} {124569} u7 {12456} {1234568} {1346}
3 {124689} {124569} {2456} {12469} {1259} {124568} {12468} 7
1 {24678} {246} 9 {2678} 3 {4678} {4678} 5
{46789} {2346789} {23469} {2568} {25678} {25} {146} {1346789} {13469}
5 {36789} {369} 1 {678} 4 {678} {36789} 2
2 {134679} {134569} {45} {1349} {159} {14567} {14679} 8
{4679} {1345679} {134569} {2458} {1234589} {1259} {12456} {1245679} {1469}
{49} {1459} 8 7 {12459} 6 3 {12459} {149} 
The candidate twos in rows 1 and 9 are all in the same columns as the blue numbers. You can eliminate the candidate twos from row 3 columns 2, 5 and 8 and row 4 columns 2 and 5. Whichever cell the two in row nine occupies will eliminate all other nines from the column, leaving the remaining twos in row 1 to form a blue finned xwing with the remaining blue numbers.
I hope some of my fellow explosion fans will find these descriptions interesting and useful.
Happy exploding!
Brian. 

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Glyn Major Major Major
Joined: 16 Jan 2007 Posts: 92 Location: London

Posted: Fri Aug 31, 2007 6:01 pm Post subject: 


A very interesting post Brian, here is my take on these examples.Well done for spotting them that's the hard part. I usually just plug away with the simple moves more times than go for the throat on the Explosion.
I think all these structures would be classified as Mutant Fish without fins. I've described them in terms of the cover and base sectors used in 'The Ultimate Fish Guide'. http://www.sudoku.com/boards/viewtopic.php?t=4993 They don't discuss variants much over there though. Try colouring the cover sectors in one colour and then flip the colour of the base sectors. The cells that don't flip lie outside the intersection and can be eliminated.
Mutant Xwing
The 6 cells 125c58 contain all the cells of the 2 base sectors (Row 1 and Centre Dot).
They are wholly contained in the 2 cover sectors (Columns 5 and 8) with 8 cells and the eliminations take place in the 2 cells at r46c5.
As an AIC in 3 it could be expressed as r25c5=r25c8r1c8=r1c5 => r46c5<>3.
Example 1 (Mutant Swordfish in 5)
The 13 cells r1289c258+r5c5 contain all the cells of the 3 base sectors (Rows 1,9 and Centre Dot).
They are wholly contained in the 3 cover sectors (Columns 2,5 and 8) with 19 cells and the eliminations take place here in the 6 cells at r37c258
Example 2 (Mutant Swordfish in 8)
The 10 cells r2c128+r5c12458+r8c45 contain all the cells of the 3 base sectors (Columns 1,4 and Centre Dot).
They are wholly contained in the 3 cover sectors (Rows 2,5 and 8) with 12 cells and the eliminations take place here in the 2 cells at r25c7.
Example 3 (Mutant Swordfish in 2)
The 12 cells r12c258+r5c25+r89c58 contain all the cells of the 3 base sectors (Rows 1,9 and Centre Dot).
They are wholly contained in the 3 cover sectors (Columns 2,5 and 8) with 17 cells and the eliminations take place here in the 5 cells r3c258+r4c25.
All the best
Glyn _________________ I have 81 brain cells left, I think. 

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