## Jigsaw Generalized x-wing

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Jigsaw Generalized x-wing

I was searching a long time to find an example of a JS which rated exactly 6.5(Generalized x-wing) and was surprised today when evaluating, a JS with ER 2.9 I generated with the last available version of JigsawExplainer, with an older version I downloaded on 13 october 2020 which was not using generalized intersection at that moment.
Result when generated:
Code: Select all
..5.........4.....3....5.........1.4..1..2........372.......4.....8....9.8....3.2 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2

Older version:
2021-01-11.png (95.08 KiB) Viewed 205 times

Yesterday I already found an example with the same shape, also rated 2.9 with the newest version and 3.2 (x-wing) with the one of october.
I solved it by hand and found a naked quad, resulting in a hidden pair and finally the x-wing, which reduced the puzzle to pointing/claiming and naked/hidden subsets(max triple).
Code: Select all
......73....1..58..2........7.....2.......8..........5..9.6.....8...6.......2.... 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2

So in the search of examples replacing generalized intersection by x-wing, I found the example above which replaced 2 generalized intersections, the first by x-wing and the second by generalized x-wing.
Is there a way to generate similar examples?
One possible solution is probably extending the fiendish rating(2.6 to 6.0) to 6.5 including generalized x-wings?
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Generalized x-wing

urhegyi wrote:I was searching a long time to find an example of a JS which rated exactly 6.5(Generalized x-wing) and was surprised today when evaluating, a JS with ER 2.9 I generated with the last available version of JigsawExplainer, with an older version I downloaded on 13 october 2020 which was not using generalized intersection at that moment.
Result when generated:
Code: Select all
..5.........4.....3....5.........1.4..1..2........372.......4.....8....9.8....3.2 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2

With Generalized Intersection with SER=2.9 also I found the solution, but also needed a naked triple of SER=3.6
urhegyi wrote:Yesterday I already found an example with the same shape, also rated 2.9 with the newest version and 3.2 (x-wing) with the one of october.
I solved it by hand and found a naked quad, resulting in a hidden pair and finally the x-wing, which reduced the puzzle to pointing/claiming and naked/hidden subsets(max triple).
Code: Select all
......73....1..58..2........7.....2.......8..........5..9.6.....8...6.......2.... 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2

So in the search of examples replacing generalized intersection by x-wing, I found the example above which replaced 2 generalized intersections, the first by x-wing and the second by generalized x-wing.

For this a found a solution with standard Naked/Hidden Pairs/Triples/Quads, and pointing/claiming and Turbot Fish (Skyscrapers and TurbotCrane) ; but without a generalized X-Wing
Highest SER = Hidden Quad = 5.6
Hidden Text: Show
Code: Select all
Eliminated candidates per SER and per Sudoku

Method    \ Sudoku |   SER |     1
|-------|------
Not counted elims  |     0 |   104
Naked Singles      |   0.1 |    27
Hidden Singles     |   0.2 |    83
Naked Pair    [2]  |     3 |     6
Naked Triple  [3]  |   3.6 |     6
Hidden Quad   [5]  |   5.4 |     6
Locked Singles[2]  |   2.8 |    18
Turbot Fish [4]  |   4.4 |    14
|-------|------
Eliminated Cand's  |   264 |   264
Sum(SER * Cand's)  | 203.3 | 203.3

Initial Candidates :   264
Maximum SER rating :   5.4
Labour rating      : 203.3

urhegyi wrote:Is there a way to generate similar examples?
One possible solution is probably extending the fiendish rating(2.6 to 6.0) to 6.5 including generalized x-wings?

Here is one with a standard X-wing [SER=3.2] (and a hidden quad [SER=5.4] and without Generalize Intersection [SER=2.9], that also will produce a solution!!)
Code: Select all
#1//B4,JS
..1......3..68..............3.1........35..2......3....5.9........2..675...74..1.
122223333111122233145166223145166663745555563744448568799448568779998888777799998
Last edited by Hajime on Mon Jan 11, 2021 5:58 pm, edited 1 time in total.

Hajime

Posts: 713
Joined: 20 April 2018
Location: Netherlands

### Re: Jigsaw Generalized x-wing

After two 2.9 rated examples I found one with 4.5 rating and allways the same shape.
Code: Select all
......73....1..58..2........7.....2.......8..........5..9.6.....8...6.......2.... 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2
..5.........4.....3....5.........1.4..1..2........372.......4.....8....9.8....3.2 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=2.9/1.2/1.2
...9....1......2.33....5..........4.........6.....9.......5....6.....7........... 122223333111122233145166223145166663745555563744448568799448568779998888777799998 ED=4.5/1.2/1.2

I will test it in SiSeSuSo later today.
urhegyi

Posts: 538
Joined: 13 April 2020

### Re: Jigsaw Generalized x-wing

urhegyi wrote:So in the search of examples replacing generalized intersection by x-wing, I found the example above which replaced 2 generalized intersections, the first by x-wing and the second by generalized x-wing.
Is there a way to generate similar examples?
One possible solution is probably extending the fiendish rating(2.6 to 6.0) to 6.5 including generalized x-wings?

I generate lots of Diabolical jigsaws (all techniques enabled) and filter on what techniques I'm looking for.
I think to catch ED=6.5 you can enable all techinques up to and including 'Forcing Chains & Cycles', generate jigsaws, and then filter as above.
The process of finding nice sudokus/jigsaws is usually a long and tedious effort, e.g.
Out of about 2000 generated jigsaws, about 40 were ED=6.5 (Generalized X-Wings), of which only these did not require Generalized Intersections:
Code: Select all
.78.25..9.6...........7...8..52.......9.8.1.......72..6...1...........6.9..36.42. 111222333111123333411222335446626655444626555444666555777789999777888999778888899 23 ED=6.5/1.2/1.2
...2....9.......6.1.2.4.8....93....4.1..6..5.6....89....8.9.6.7.3.......4....7... 111122333111122233144442233445452233445555566775758666777778866799998886999998886 23 ED=6.5/1.2/1.2
......5.3..7.1.25..19........6.4..9...........7..2.6........34..51.3.9..3.4...... 112222222112333332111133334551666644555564444556666744588887777988888977999999977 22 ED=6.5/1.2/1.2
32...........2.17......75.......8...85.....41...4.......89......94.5...........26 111122222113344422133344442133555442133555667899555667899996667889996677888887777 20 ED=6.5/1.7/1.7
3.5...9....7.2.3...2...........4.6..9.......5..6.5...........6...1.3.2....2...5.7 111222233111222233114452333144455633444555666774556668777956688779999888779999888 20 ED=6.5/1.2/1.2
.1.67...35.......8...2..1......91...............46......9..3...1.......73...85.6. 112222222112333332111133334551666644555564444556666744588887777988888977999999977 20 ED=6.5/1.2/1.2
2......7..1..26...5..9.......6...3..7.......9..2...5.......4..1...28..5..9......6 111123333111123333144422223444555622744555662774555666877776669888879999888879999 20 ED=6.5/1.2/1.2
......6.....28.......6...4.9.4.....35.......63.....9.2.6...1.......29.....1...... 111223333112223433112225433611525444666555444666575884996577788996977788999977888 18 ED=6.5/1.2/1.2

1to9only

Posts: 3416
Joined: 04 April 2018