Let me try a somewhat unconventional way of explaining Swordfish. First, since you understand x-wing, lets look at an example:
Code: Select all
.---------------------.---------------------.---------------------.
| 1678 167 4 | 178 178 9 | 3 5 2 |
| 18 3 2 | 4 6 5 | 7 18 9 |
| 9 157 578* | 12378- 12378- 138* | 6 18- 4 |
:---------------------+---------------------+---------------------:
| 5 147 78* | 138- 1348- 138* | 2 9 6 |
| 16 2 3 | 5 9 16 | 8 4 7 |
| 468 46 9 | 268 248 7 | 5 3 1 |
:---------------------+---------------------+---------------------:
| 37 9 1 | 378 378 2 | 4 6 5 |
| 347 457 57 | 1367 137 136 | 9 2 8 |
| 2 8 6 | 9 5 4 | 1 7 3 |
'---------------------'---------------------'---------------------'
and lets focus on the number 8. Careful study of the grid will reveal an x-wing in r34c36, eliminating 8 from r3c458 and r4c45. But let's take another look at this deduction. Let us write down all of the different places one can find 8 in the different columns:
C1 : (126)
C2 : (9)
C3 : (34)
C4 : (13467)
C5 : (13467)
C6 : (34)
C7 : (5)
C8 : (23)
C9 : (8)
For example C4 : (13467) means you can find an 8 in column 4 in rows 1,3,4,6,7.
Forget about the original grid and only look at this column of numbers. If this was a sudoku column, you would say, "hey, there's a naked pair (34),(34) in C3 and C6," and then you would eliminate 3 from C4,C5,C8 and 4 from C4,C5. But if you translate everything back to the sudoku grid, these are exactly the deductions of the x-wing, and for that matter, the naked pair exactly corresponds to the cells of the x-wing. This is not a coincidence.
Every (column based) x-wing will correspond to a naked pair when you write down the where entries can go in a column. If you are using SudoCue, copy in this puzzle and switch the view to CN-view. Look at row 8. You will see exactly the list I gave above.
Now let's move on to swordfish. If an x-wing corresponds to a naked pair, then a swordfish must correspond to a naked triple. Let's see an example:
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*-----------------------------------------------------------*
| 35 18 35 | 4 7 9 | 6 2 18 |
| 178 178 4 | 26 26 18 | 3 9 5 |
| 9 2 6 | 35 18 35 | 148 47 1478 |
|-------------------+-------------------+-------------------|
| 57 3 1 | 257 248 578 | 45 6 9 |
| 258 48 25 | 9 3 6 | 145 47 147 |
| 567 467 9 | 157 14 157 | 2 8 3 |
|-------------------+-------------------+-------------------|
| 23 5 23 | 8 9 4 | 7 1 6 |
| 4 16 8 | 37 16 37 | 9 5 2 |
| 16 9 7 | 16 5 2 | 48 3 48 |
*-----------------------------------------------------------*
In this puzzle, we will focus on the number 1.
Let's write down where the 1's can go in each column (or we use the CN-view of SudoCue to do the same job)
C1 : (29)
C2 : (128)
C3 : (4)
C4 : (69)
C5 : (368)
C6 : (26)
C7 : (35)
C8 : (7)
C9 : (135)
Here we have to look a little harder, but eventually we spot the naked triple (29), (69), (26) in C1,C4,C6. This allows us to eliminate 2 from C2 and 6 from C5. In the original grid, this corresponds to removing 1 from r2c2 and r6c5.
Code: Select all
*-----------------------------------------------------------*
| 35 18 35 | 4 7 9 | 6 2 18 |
| 178* 178- 4 | 26 26 18* | 3 9 5 |
| 9 2 6 | 35 18 35 | 148 47 1478 |
|-------------------+-------------------+-------------------|
| 57 3 1 | 257 248 578 | 45 6 9 |
| 258 48 25 | 9 3 6 | 145 47 147 |
| 567 467 9 | 157* 14- 157* | 2 8 3 |
|-------------------+-------------------+-------------------|
| 23 5 23 | 8 9 4 | 7 1 6 |
| 4 16 8 | 37 16 37 | 9 5 2 |
| 16* 9 7 | 16* 5 2 | 48 3 48 |
*-----------------------------------------------------------*
For more information on this approach, see this
thread on the player's forum.
By the way, the reason why I like this approach is that it makes it much easier to spot these patterns and extend the pattern. For instance, you can probably guess that a jellyfish will correspond to a naked quad. The downside of the approach (especially if you're working on paper) is that you might have to right down all of these columns and that can be downright boring. Moreover, sometimes it's hard to see the connection between the column output and the original grid. But, it's food for thought and perhaps somebody else will offer up a more conventional explanation.