dailysudoku.com

[someone_somewhere]

Hi,
Anyone interested in a couple of 19 numbers positions that can be solved only with the advanced technique XY-Wing? (or mybe some other even higher [guessing] technique)

Just let me know.

see u,

[someone_somewhere]

Sorry, let's make it harder 17 cells Sudoku!

waiting for volunteers,

[Katie]

I'm always ready to try. Send me the details via the post message system, and I'll have a go (gulp)

[someone_somewhere]

This is just for Katie.
Nobody is allowed to solve it ... ;-)

- - - 1 - - - 7 -
- 4 - - 9 - - - -
- 2 - - - - - - -
7 - - 8 5 - - - -
- - - - 2 - 4 - -
3 - - - - - - - -
- - - - - - 2 - 1
- - - 3 - - 6 - -
5 - - 7 - - - - -

after 34 numbers it gets interesting.

see u,

[Katie]

Hope this is right.

8 6 5 1 3 4 9 7 2
1 4 7 2 9 5 3 6 8
9 2 3 6 7 8 5 1 4

7 9 4 8 5 3 1 2 6
6 5 1 9 2 7 4 8 3
3 8 2 4 6 1 7 9 5

4 7 9 5 8 6 2 3 1
2 1 8 3 4 9 6 5 7
5 3 6 7 1 2 8 4 9

Did take me about 90 minutes though.

I'd enjoy more of these. Thanks

[someone_somewhere]

Hi Katie,
Yup, the solution is Ok.

After the "forplay" you can find with the usual techniques, up to 34 numbers, getting to the position:

- - - 1 3 4 - 7 2
- 4 7 2 9 5 3 - -
- 2 3 6 7 8 5 - -
7 - 4 8 5 3 1 2 -
- - - 9 2 7 4 - 3
3 - 2 4 - - 7 - 5
4 7 - 5 8 - 2 3 1
2 - - 3 4 - 6 5 7
5 3 - 7 - 2 - - -

which is the G-point of the game.
Here you can continue with a XY-wing combination starting from r2c1
and getting to eliminate 6 from r5c8.
If someone can to it better and quicker and nice, please don't keep it for yourself.

One more time, a big BRAVO for Katie. The lady is a Pro!

(Sorry, I had to correct the prev. message)

see u,

[alanr555]

Given that Katie has now solved this one, is it possible to explain?

I have worked through to the [30 to go] stage - leaving the following
solution grid (omitting resolved cells)

689; 568; 58; - - -; 89 ; - -
18; - - - - - -; 16; 68
19; - - - - - -; 149; 49
-; 69; - - - - - - ; 69
68; 15; 15; - - - -; 68; -
-; 89; - -; 16; 16; -; 89;-
- -; 69; - -; 69; - - -
-; 18; 189; - -; 19; - - -
- -, 16; - ; 16; -; 89; 49; 489

This is a "closed" set in that no digit appears without a mate in any row,
column or block and the number of unique digits in any row, column or
block is equal to the number of cells.

I am not proficient in "swordfish" but from my understanding of it, all
the chains have been used already in reaching the above - so that
A1/E1/E8/B8/B9/D9/D2/A2/A1 or G3/G6/F6/F5/J5/J3/G3 do not yield any
new information or lead to new exclusions.

How does XY-Wing from r2c1 lead to elimination of 6 from the 68 in r5c8?
I presume that "8" is the linking digit and notice that several rows and
columns contain more than two occurrences of digit 8.

r2c1, r2c8, r2c9 form a triplet set {18,16,68} and interesects with the
column 8 quintet set {16,149,68,89,49} with {16} as the link point.

The 6 in r5c8 can be eliminated if r2c8 (the link point) resolves to 1 from
the possibility set at 16. I do not understand, at present, why one would
be able to reach that conclusion. Enlightenment appreciated!!

Alan Rayner BS23 2QT

[Guest]

hi alanr555

As someone_somewhere said using the Xwings to solve the problem:

r2c1 can be 1 or 8
if r2c1=1 --> r2c8=6--> r5c8 cannot be 6
if r2c1=8 --> r5c1=6--> r5c8 cannot be 6

so you can eliminated 6 in r5c8.
Hope this can help.

[alanr555]

> As someone_somewhere said using the Xwings to solve the problem:

> r2c1 can be 1 or 8
> if r2c1=1 --> r2c8=6--> r5c8 cannot be 6
> if r2c1=8 --> r5c1=6--> r5c8 cannot be 6

> so you can eliminated 6 in r5c8.

Since writing in this forum, I have discovered how it works.

1) Identify a rectangle in the solution grid where three corners
involve only three digits and only two in each corner.

(here r2c1=18, r5c1=68, r2c8=68 involves only 1,6,8)

2) Consider the fourth corner. If it contains a digit that is NOT in the
opposite corner but IS one of the three digits above, then this
digit can be excluded.

(here the fourth corner is r5c8. It does not matter how many digits
it holds - whether they be 1,6,8 or others!
Digit 6 is part of the trio {1,6,8} but is NOT in the opposite corner
- which is r2c1 in this case. Thus 6 can be excluded from r5c8.

+++

Of course, the difficult part is identifying the rectangle!

I find that rewriting the solution grid with only the UNresolved cells
can assist in presenting a new view to the brain and allow the pattern
to be spotted that much more easily (I use a hyphen to represent the
space of a resolved cell). Of course this is useful only when one has
reduced the solution grid to a relatively small number of cells.

+++

I found that using the nomenclature of XY-Wing was confusing and
somewhat off-putting. We need a new name. One suggestion might
be "rectangular trio".

Thanks for the assistance in clarifying the generality of it.
Alan Rayner BS23 2QT

[keith]

Whoops!

I just solved this one without having to resort to swordfish or xwings - I just used my regular technique. I'll have to redo the puzzle and check my logic - maybe I made a logical error but got the correct answer.

What should I do? My current plan is to post every step and ask for challenges on the logic. It might take me a few days to document my solution.

Best wishes,

Keith