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METHODS

Single Candidate
Intersections
Naked
Hidden
Fish
X-Wing
Sword-Fish
Jelly-Fish
Squirm-Bag
XY-Wing

 SINGLE CANDIDATE When a candidate is present only once in the line, column or in the block, this is certainly the right place to insert the number. In the example above the candidate 5 is only present in the green marked cell of the block and could be a number without any doubt.

 INTERSECTIONS If a block is having one or more candidates in only one line or column, the candidates can remove themselves from other remaining  blocks in the same line or column. In the example, the candidate 9 in block 2 on the second line (R2C4 & R2C5) is excluding the other candidates of the line on different blocks. So the candidate 9 could be removed by R2C2. Sometimes a candidate inside a line or column is present in only one block. From the moment one of those cells got to have that candidate, then we can exclude from the remaining cells in the same block. Example: in R1 the candidate 9 is present in C2 & C3 (yellow). The candidates with 9 could be eliminated in the same block (red).

 NAKED If two or more cells in one line, column or block are having the same candidates and only them, then no other cells in that region can have those  candidates. Well, the candidates could be excluded from the other cells of the region. Example: In R1C7 & R1C8 la couple {79} eliminate the candidates {7} & {9} from the other cells of the line. {2589} will become {258}, {5789} will become {58} Very often it's difficult to recognize the triplet or quad, but anyway it's a good way to eliminate the candidates. Follow another detail of the previous example: the naked triplet on block {379}; it's eliminating the candidates {379} on the block from red cells.

 HIDDEN If two or more cells in one line, column or block are having the same candidates, but not only them, then the other candidates could be removed. In the example above the canidates 1 & 4 are highlighted on the second line (also on the third block) in yellow. They are certainly in these positions even it's not know where would be the one and the other, but for sure the candidate 9 wouldn't be in R2C8 and the candidates {39} in R2C9 as they could be removed.

 FISH This is a generic methodology that includes the similar technique which is applicable in a different way to the dimension of the grid. X-WING consists in searching the couples of the candidates in the entire grid on the lines or column, that forms a quadrilater. It is possible to exclude the internal or external candidates in the vertices. In the example above the candidate 4 is highlighted on the grid. In the column C2 & C4 the couples are present and aligned in R5 and R8 are highlighted in yellow, which can eliminate the candidates they are having (red). Another example of X-WING on the lines with the candidate 7, could be removed from red cells. SWORD-FISH is an extension of X-WING. You got to search three couples or triplets of candidates on the entire grid aligned on the lines or columns. In the example the highlighted candidate is 6. The yellow cells on R5 R7 and R9 identify the Sword-Fish on the lines, and those red one identify the cells from where the candidate should be removed on the  basis of the knots of the columns C1, C3 and C7 The previous example we should see like this, to understand better the area interested by Sword-Fish. Another example is shown bellow with application one the columns.. JELLY-FISH - It's identical with the technique of  Sword-Fish, but it's applied in 4 lines or columns instead of  3. Here is an example of Jelly-Fish with the candidate 9 on the columns C1, C2, C4 and C6. The knots on the lines are R1, R2, R7 and R9. The candidates 9 could be removed from the red marked cells. To avoid confusion, look at the Jelly-Fish grid as it appears bellow: