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 x-wing”.
Eureka! If there is such a thing as a ”Blue finned x-wing” 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 Franken-fish. 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: Select all
{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}
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: Select all
{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
Blue finned x-wing.
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: Select all
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}
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: Select all
{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}
Example 2
Code: Select all
{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}
Example 3
Code: Select all
{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}
I hope some of my fellow explosion fans will find these descriptions interesting and useful.
Happy exploding!
Brian.