For a particular row,column or zone, it can be deduced that there is only one possible cell that a value can be entered.

This may be due to other cells being populated in that row,col or zone, or it may be that the same value appears in another column or row that would prevent the value from being entered anywhere else.

Either way, each of these cells can be "marked off" in turn, leaving only one possible candidate for a particular value.

In the example left, the only possible cell for value 1 would be row 8 col 2.

This is slightly different. For a particular cell, you may deduce that no other value could possbily be entered into that cell.

This is because, every other value already appears in that zone, row or column.

In the case left, only the number 3 could be entered into row 5 col 3.

The naked subset is the first, and most basic elimination technique in Sudoku. Most people will actually be using this technique, although they may have a different term for it, or have not even thought about at all. The basic premise is this:

If a number of cells in a unit (row,col, or zone) contain exactly the same number of candidates between them, then these candidates can be removed from every other cell in that unit.

In the example left, the candidates are shown against each cell. In column 8 (highlighted) you can see the following candidates:

{4}{2,5,9}{6}{1,3,5,9}{2,5,9}{1,2,3,5,9}{7}{5,9}{8}.

You will notice the candidates 2,5 and 9 are the only values in the following candidate sets: {5,9}{2,5,9}{2,5,9} Although you do not know exactly where 2,5 and 9 go, you know it must be within these three cells, and can therefore be eliminated from the cells {1,3,5,9}{1,2,3,5,9}.

This leaves the column candidates as: {4}{2,5,9}{6}{1,3}{2,5,9}{1,3}{7}{5,9}{8}.

A more familiar example may be a naked pair i.e. {1,6}{1,6}, but in fact, naked subsets can be found in 2s,3s, or 4s (naked quads).

The hidden subset is very similar to the naked subset, but instead of eliminating candidates from other cells, outwith the subset, values are eliminated from the cells that contain the hidden subset.The definition is as follows:

If a number of cells in a unit (row,col, or zone) contain between them, the same number of candidates, then all other values can be eliminated as a potential candidate for these cells.

In the example left, the candidate set for zone 6 is {2,8}{4}{2,5}{6}{1,3,8}{1,3,5}{2,8,9}{8,9}{7}.

Now, it may not be immediately apparent (hidden subsets never are!) but from the highlighted cells, we can see that the numbers 1,3 and 5 appear only in 3 cells (in bold). We can therefore deduce that, no other numbers could possibly go in any of these cells, other than 1,3 and 5. This means we can eliminate the number 2 from {2,5}, and the number 8 from {1,3,8}.

This leaves the candidate set as {2,8}{4}{5}{6}{1,3}{1,3,5}{2,8,9}{8,9}{7} and we can can now add the number 5 to row 4, col 9.

As a footnote, we can now see there is a naked subset consisting of {2,8}{2,8,9}{8,9}.

Other wise know as block/row or block/column intersections, a unit intersection is where one unit type (row, column, zone) crosses another unit type. Technically, this could be row/col or zone/row or zone/col, but for elimination purposes we need only consider where a row or column crosses a zone.

The definition is as follows: If a candidate must appear where two units intersect, then that candidate may be eliminated from every other cell outwith that intersection.

To explain better, take the example on the left. The value 1 must appear in column 8 (blue) somewhere, as by definition, each value must appear once in every row,column or zone. As you can see, it also must appear where column 8 crosses zone 6, as the column cells outwith that zone, do not have 1 as a valid candidate: {4}{2,5,9}{6} and {7}{5,9}{8}.

Therefore 1 can only appear where column 8 intersects with zone 6, and can be eliminated from all other cells in that zone, specifically row 6, col 7 and row 6, col 9.

Note - the intersection can work the other way around. For example, we may find that the value 2 must appear where zone 6 meets column 8, and can therefore be eliminated from the other cells in column 8.

X-wing is a elimination technique that arises when two columns have exactly two remaining cells for a particular candidate. These cells must share the same rows also, giving rise to the "X" shape that gives the technique it's name.

The diagram on the left shows a typical scenario. Columns 2 and 6 both have two remaining cells in which the candidate 7 can be placed. This means either the 7 is in R1C2 and R7C9 OR it is in R9C2 and R1C8, i.e. they are diagonally apart.

Either way, a 7 must exist in both rows (in two of the four cells listed above). This means 7 cannot be in any other cell in both rows, and can be eliminated. In this example, the 7 is eliminated from R1C3 and the number 8 can be entered.

The definition is therefore as follows:

For a particular candidate: If there exists two columns with exactly two remaining cells in which to place the candidate AND these cells share the same rows, then the candidate can be eliminated from all other cells in the two rows.

As with most of the techniques ,the rows and columns in the above description can be interchanged (i.e. the "X" shape could 'lie' on it's side).

Swordfish is essentially the same as the X-wing, but this time applies to 3 rows or columns.

In the example, left you will see there are 3 rows where the number 2 must be placed. Using the logic for the X-wing, you can see that it can be eliminated from all three columns that connect these rows. This means it can be eliminated from R3C7, and the number 5 can be entered there.

If you cannot see how this works, try putting in a 2 in one of the cells in row 2 and follow from there. Then try again using the other cell, and see how the puzzle ends up. Either way you'll find that there will always be a 2 in column 7 which is why it can be eliminated from the cell highlighted yellow.

(This is not unlike the method of colouring which will be documented soon)

Jellyfish is simply this technique expanded to 4 rows/columns.

Please note - when giving a hint, I refer to Swordfish as "X-wing triple", and Jellyfish "X-wing quad".