http://forum.enjoysudoku.com/the-ultimate-fish-guide-t4993.htmlis another guide people use for constructing fish:
However practically from a manual solver perspective can be easily lost in translation
this presentation is the easiest i can describe for your consumption
something akin to this
postconsider the normal Mark up of a grid in spacial definitions Refereed to as
RC markup which stands for the Row,Col Position listing N where N is the solved Value of the "Grid"
Some Might list the Potential placements {pencil marks}
Pencil marks aren't derived how you think they are
Pencil Marks are derived From the spaces:
Row Number Listing Col
Col Number Listing Row
Box Number : listing Square
which are the positions left "ON" by placements of N in R,C as each placement turns off 8 locations in box,row and col
when Rn,Cn,Bn, space is combined with RC we Now see the original Grid + Potential markups
Rn,Cn, space is where we find basic Fish and yes most of the time very few are full constructs.
how does this work?
here is the PM Grid view
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.-----------------------.-----------------.------------.
| 1 679 8 | 5 679 79 | 2 3 4 |
| 5 469 469 | 3 469 2 | 1 7 8 |
| 247 2347 2347 | 8 147 147 | 5 6 9 |
:-----------------------+-----------------+------------:
| 8 124 124 | 6 124 5 | 7 9 3 |
| 267 267 5 | 9 237 37 | 4 8 1 |
| 3 1479 1479 | 14 147 8 | 6 5 2 |
:-----------------------+-----------------+------------:
| 9 8 47 | 2 45 6 | 3 1 57 |
| 2467 1234567 123467 | 14 13459 1349 | 8 24 567 |
| 246 123456 12346 | 7 8 134 | 9 24 56 |
'-----------------------'-----------------'------------'
lets convert this grid to an Rn,Cn,Bn view
my linked picture lets focus on the Row - # x col
https://www.mediafire.com/view/4a5lha1da5xdohr/Capture4.JPG#top down is the Row {0 - 8}
left to Right represents the "Digit" 1 - 9
stored Cells is the Col the digit is found in
how to use these spaces
if you like "drawing lines" or slicing this is what you are doing with lines each line you draw marks a "hit" on cells thats how the Digit you are evaluating
in a Row sword fish are operating you are drawing lines down the Columns to see how many hit with at most 3 per col
focus on Digit "4"
in my chart
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R Digit {4}
0 |
1 | 1 2 4
2 | 0 1 2 4 5
3 | 1 2 4
4 |
5 | 1 2 3 4
6 | 1 2
7 | 0 1 2 3 4 5 7
8 | 0 1 2 5 7
we are looking for 3 rows with exactly the same "set" or sub set with max of 3 Cols listed
which happens in Row 1,3,6 as they all contain exactly the set of {1,2,4}
which produces: {in hodoku}
Swordfish: 4 r247 c235 => r3c235,r6c235,r8c235,r9c23<>4
in the view of Rn space the Rows that haves [124] are locked for digit "4" and all other Rows cannot use [1,24]
which updates to this:
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R Digit {4}
0 |
1 | 1 2 4
2 | 0 5
3 | 1 2 4
4 |
5 | 3
6 | 1 2
7 | 0 3 5 7
8 | 0 5 7
next example is :
using the Cn space Digit "4" you should be able to spot the
Swordfish: 4 c168 r389 => r3c235,r8c2345,r9c23<>4 {in hodoku}
very easily.
this method for fish finding is also applicable to finding "subsets" and was pointed out way back in 06
check out Col (3)- #s 1, 4 both list "5,7" Row we have a hidden pair of 1,4 @ R57C3
{ has no eliminations for us but its an example}
Bn space isn't the easiest one to utilize effectively which is why non basic fish aren't as easy to translate
It seems to be related to the simple way of identifying Empty Rectangles with one vertical and one horizontal line.
easy sure
look at box 2 digit 4
Draw a line down Col 5
Draw a line across Row 3
if all the digits of Box 2 for "4" land on the lines only we have a starting box
next
for each of the Cols that intersect row 3 draw a col line if any of these cols hold 2 "4"s with 1 in the row position
{hint there isn't any}
next check the Col line for any row that has 2 "4"s with at least 1 in the col position
we find one @ row 7
mark it and we have constructed the ER
Empty Rectangle: 4 in b2 (r7c35) => r3c3<>4
for me id suggest building it backwards
first find a row or column with a Bi local for digit x
then check the boxes as described above.
