dailysudoku.com

[David Bryant]

Here's a very tough puzzle that requires use of the "Nishio" technique.

[David Bryant]

Here's another puzzle that requires the "Nishio" technique. Here's a hint -- after 13 moves, analyze the possibilities for "2".

[someone_somewhere]

Hi,
For this last one I could make 14 moves:

8 in r5c3 - Unique Horizontal
8 in r4c5 - Unique Horizontal
8 in r1c7 8 in r3c4 - Unique Horizontal
6 in r1c8 - Unique in 3x3 block
7 in r3c7 - Unique in 3x3 block
3 in r1c6 - Sole Candidate
6 in r5c9 - Unique Horizontal
9 in r5c7 - Unique Horizontal
9 in r2c9 - Unique Vertical
7 in r5c8 - Unique in 3x3 block
5 in r5c1 - Sole Candidate
2 in r5c2 - Sole Candidate
2 in r3c3 - Unique Horizontal
3 not in r2c3, it is in r3c1 or r3c2 (Row on 3x3 Block interaction)
9 not in r7c5, it is in r7c4 or r9c4 (Column on 3x3 Block interaction)
9 not in r9c5, it is in r7c4 or r9c4 (Column on 3x3 Block interaction)

And now, as you have suggested, when analyzing the "2" and only the "2"s
we get quickly to the conclusion that "2" can't be in r7c6 and it can't be in r4c6. This last one implies that "2" must be in r6c5.

But, as much as I know, this is not Nishio, but "coloring" for the number "2". So, or so, I will not argue about the name of the technique.
(Nishio should involve more than one number ...).

BTW, I could find only cases to exclude one (or several) numbers by the coloring techniques only if the number of occurences was 15, 17 or 19.
In your example there where 15 occurences of "2"s.

Thank you for the nice example.

see u,

[David Bryant]

[someone_somewhere]

Hi David,

I have reduced to the position:

[David Bryant]

[someone_somewhere]

Yes, you are right:

However you try to color the rest of the cells you will sooner or later came to a contradiction (the one of column 9 - is the shortes one).
And this means that the "initial" number (and some additional) can be excluded.

Now why do I use the word "coloring"? Because I simply isolate the graph with the number that occurs 15, 17 or 19 times in the candidate table and than start coloring from one of the numbers.
If the coloring leads to no contradiction, I take an other one (if possible not colored) and repeat the process.
It could be that every cell is in at least one coloring solution.
If I find a cell that leads to a contradiction (you called it Nishio, here) than I am happy and can take a look if he has not some relatives (conjugate cells) that can be shot too
Sometimes I "see" just one cell that is not part of the colorings that I done till that point. So I take it as a candidate to be shoot.
If he is innocent (part of a valid coloring) I let him go.

That's what I am using. Examples will follow.

P.S. the 3 cells from the above examples are (probable) called conjugates and can be ALL eliminated together.

see u,

[David Bryant]