The New Sudoku Players' Forum

[urhegyi]

Are these morphs and how do you transform them?

[Leren]

Removed. No longer necessary. Leren

[urhegyi]

I can't solve them with a windoku solver because they are windokus without the regular 3x3 sudoku boxes. They are both valid.

[Leren]

Here are your puzzles re-formatted to Sudoku puzzles (which they are).

Code: Select all

...123.....3.4.1...4.....5.3.......256.....717.......8.1.....6...5.9.8.....875...
..4...5.....123...3...4...1.3.....2..56...71..7.....8.5...9...8...875.....1...6..

If you want to learn about minlexing of Sudoku puzzles you can start here.

Even without minlexing them It appears that they are probably isomorphs, because the start of their solution signatures is identical

Both puzzles have 217 candidates after a basic clue markoff and 10 placements and 142 candidates at the conclusion of basics.

Perhaps someone else can provide the minlex form of these puzzles to prove the isomorphism.

Leren

[Hajime]

I can't solve them with a windoku solver because they are windokus without the regular 3x3 sudoku boxes. They are both valid.

See http://forum.enjoysudoku.com/windoku-solo-t41273.html
In SiSeSuSo like:

Code: Select all

#1/JS/B4
1.7...3.2...826...3.......1.1..8..3..52.7.98..7..3..2.2.......7...613...8.6...5.9
955596669711172227711172227711172227955596669833384448833384448833384448955596669


[Mathimagics]

Perhaps someone else can provide the minlex form of these puzzles to prove the isomorphism

Yes, they are isomorphic, both have the minlex form:

Code: Select all

......123..1..2....4..5..6.......657..5..7....2..8..4.1..2.....5..7.....6.93.8...

[JPF]

Here are the two puzzles:

Code: Select all

+-------+-------+-------+   +-------+-------+-------+
| . . 4 | . . . | 5 . . |   | . . . | 1 2 3 | . . . |
| . . . | 1 2 3 | . . . |   | . . 3 | . 4 . | 1 . . |
| 3 . . | . 4 . | . . 1 |   | . 4 . | . . . | . 5 . |
+-------+-------+-------+   +-------+-------+-------+
| . 3 . | . . . | . 2 . |   | 3 . . | . . . | . . 2 |
| . 5 6 | . . . | 7 1 . |   | 5 6 . | . . . | . 7 1 |
| . 7 . | . . . | . 8 . |   | 7 . . | . . . | . . 8 |
+-------+-------+-------+   +-------+-------+-------+
| 5 . . | . 9 . | . . 8 |   | . 1 . | . . . | . 6 . |
| . . . | 8 7 5 | . . . |   | . . 5 | . 9 . | 8 . . |
| . . 1 | . . . | 6 . . |   | . . . | 8 7 5 | . . . |
+-------+-------+-------+   +-------+-------+-------+


Apply these permutations to the first puzzle:
rows : (1 3 2) (7 8 9)
cols : (1 3 2) (7 8 9)

and you get the second one.

JPF

[Leren]

OK so that works easily in the Sudoku format (thanks to Mathimagics and JPF for proving the isomorphism in two different ways), but how would you prove the isomorphism in the Windoku Solo (WS-S) format ? Here are the two original WS-S puzzles.

Code: Select all

...3.2.....3.4.1...4.....5.1...2...3.6.5.1.7.8...7...5.1.....6...5.9.8.....7.8...
.3.....2.1...2...3...341.....4...5...56...71...1...6.....598...8...7...5.7.....8.

So how might you canonicalize a WS-S puzzle ?

Here is one suggestion. 1. Apply the W transform to a WS-S puzzle. 2. Minlex the result as per the well known Sudoku method. 3. Apply the W transform to the minlexed result. 4. Re-label the result in the obvious way.

It's not obvious to me that the result would be in minlex format overall, but at least two isomorphic WS-S puzzles will give the same result.

Leren

[Leren]

Code: Select all

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

Actually this minlexing thing in WS-S space looks really easy.

In the Sudoku view in the grid on the left, the bands and stacks are Rows and Columns 123, 456, 789. In the WS-S view in the grid on the right the bands and stacks are Rows and Columns 159, 234, 678.

With this in mind you can do all the same Band and Stack permutations plus permutations of rows and columns within bands and stacks, rotations, transpositions, re-labling etc with equal facility in both views.

Let's see if this works or I get shot down in flames.

Leren

[Serg]

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