The New Sudoku Players' Forum

[champagne]

I am pretty sure that most of the tridagons in miths file are the simple type ..[ with one guardian]
But a filter for these or without these would be useful either way !!!!
except
looking back to miths thread ... it seems he is way ahead ... on page 1 he and denis explored the min guardian and max guardian count...and the term "non-degenerative" was introduced [yuk] and posted a few puzzles with high guardian counts.... but denis alluded correctly that this very much depends on the expansion status ..

So the "simple" type [as above] is the "non-degenerated" type ?

Here is the result of a check made by "blue"
mith's list has 2,113,220 puzzles of the first type, over 28026 "starts", and 1,629,623 puzzles of the 2nd type, over 19937 "starts".

So you are likely right, this is the majority of mith's file. I am not 100% sure that they are all "non degenerative "
And yes, if I study puzzles with the type 1 or 2 seen in the start PM, the case "after easy moves " has to be considered.

[coloin]

I didnt think that the "starts" had anything to do with the guardians.
you mentioned there were 2 "starts" as did blue...
so these six may well be just 2 ED

Code: Select all

... ... ...        ... ... ...         ... ... ...         ... ... ...
... ... ...        ... ... ...         ... ... ...         ... ... ...
... ... ...        ... ... ...         ... ... ...         ... ... ...
                                                                     
... ..x x..        ... ..x x..         ... ..x x..         ... ..x x..
... .x. .x.  -->   ... .x. .x.         ... .x. .x.         ... .x. .x.
... x.. ..x        ... x.. ..x         ... x.. ..x         ... x.. ..x
                                                                     
... x.. z..        ... x.. z..         ... x.. z..         ... x.. ...
... .x. .z.        ... .x. .z.         ... .x. ...         ... .x. .z.
... ..x ..z        ... ..x ...         ... ..x ..z         ... ..x ..z
                                                                     
and                                                                   
                                                                     
... ... ...        ... ... ...         ... ... ...         ... ... ...
... ... ...        ... ... ...         ... ... ...         ... ... ...
... ... ...        ... ... ...         ... ... ...         ... ... ...
                                                                     
... ..x x..        ... ..x x..         ... ..x x..         ... ..x x..
... .x. .x.  -->   ... .x. .x.         ... .x. .x.         ... .x. .x.
... x.. ..x        ... x.. ..x         ... x.. ..x         ... x.. ..x
                                                                     
... x.. .z.        ... x.. ...         ... x.. .z.         ... x.. .z.
... .x. ..z        ... .x. ..z         ... .x. ...         ... .x. ..z
... ..x z..        ... ..x z..         ... ..x z..         ... ..x ...


The "starts" envolve the same 3 clues in B1B2B4 [B5B6B8 above] with .. 2 clues in box 5 [B9 above ] ....
Below, there are [at least] 8 ways to have 2 clues in B5 .... but the guardian clue is the diagonal 3rd clue in B5 .. and is not one of the 3 tridagon clues

2 ways to have 3 diagonal clues in B1B2B4

Code: Select all

..12......2..3....3....1...2.........1.........3.................................
..13......2..1....3....2...2.........1.........3.................................

and 4 ways each to have 2 clues in B5 [in the tridagon pattern which excludes a diagonal third clue]

Code: Select all

..12......2..3....3....1...2..1......1..2......3.................................
..12......2..3....3....1...2..3......1.........3..2..............................
..12......2..3....3....1...2...1.....1...3.....3.................................
..12......2..3....3....1...2.........1...3.....31................................
                                                                                 
..13......2..1....3....2...2..1......1..2......3.................................
..13......2..1....3....2...2..1......1..3......3.................................
..13......2..1....3....2...2....3....1.2.......3.................................
..13......2..1....3....2...2....1....1.........3.2...............................

[blue]

Here is the result of a check made by "blue"
mith's list has 2,113,220 puzzles of the first type, over 28026 "starts", and 1,629,623 puzzles of the 2nd type, over 19937 "starts".

I need to revise those numbers down a bit:
2,078,802 puzzles of the first type, over 26640 "starts", and 1,625,604 puzzles of the 2nd type, over 19672 "starts".

[coloin]

so these six may well be just 2 ED

Code: Select all

..12......2..3....3....1...2..1......1..2......3.................................#1
..12......2..3....3....1...2..3......1.........3..2..............................#2
..12......2..3....3....1...2...1.....1...3.....3.................................#3
..12......2..3....3....1...2.........1...3.....31................................#4
                                                                                   
..13......2..1....3....2...2..1......1..2......3.................................#5
..13......2..1....3....2...2..1......1..3......3.................................#6
..13......2..1....3....2...2....3....1.2.......3.................................#7
..13......2..1....3....2...2....1....1.........3.2...............................#8
                                                                                   
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#1
...................................X.....X.X.....X.X.......XX......X..X....X....X#2
...................................X.....X.X.....X.X.......XX......X..X....X....X#3
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#4
                                                                                   
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#5
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#6
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#7
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#8


Indeed there are 2 ED patterns !!!! but it is far from obvious !

to confuse everyone furthur .. the 14 ED ways for the clues making up the 12 tridagon clues have 5 ED patterns

Hidden Text: Show

Code: Select all

..12......2..3....3....1...2..1.3....1..2......3.................................# 1
..12......2..3....3....1...2..1......1.32......3.................................# 2
..12......2..3....3....1...2..1......1..23.....3.................................# 3
..12......2..3....3....1...2..31.....1.........3..2..............................# 4
..12......2..3....3....1...2..3......1.........31.2..............................# 5
..12......2..3....3....1...2..3......1.........3.12..............................# 6
..12......2..3....3....1...2.........1...3.....31.2..............................# 7
..13......2..1....3....2...2..13.....1..2......3.................................# 8
..13......2..1....3....2...2..1.3....1..2......3.................................# 9
..13......2..1....3....2...2..1......1..23.....3.................................#10
..13......2..1....3....2...2..1......1.23......3.................................#11
..13......2..1....3....2...2..1......1..3......32................................#12
..13......2..1....3....2...2..1......1..3......3.2...............................#13
..13......2..1....3....2...2...31....1.........3.2...............................#14

...................................X.....X.X....XX.X.......X.X.....X...X...X..X..# 1
...................................X.....X.X.....XXX.......X..X....X.X.....X...X.# 2
...................................X.....X.X....XX.X.......X..X....X..X....X..X..# 3
...................................X.....X.X....XX.X.......XX......X...X...X...X.# 4
...................................X.....X.X.....XXX.......XX......X..X....X....X# 5
...................................X.....X.X....XX.X.......XX......X...X...X...X.# 6
...................................X.....X.X.....XXX.......X..X....X.X.....X...X.# 7
...................................X.....X.X.....XXX.......X..X....X.X.....X...X.# 8
...................................X.....X.X....XX.X.......X.X.....X...X...X..X..# 9
...................................X.....X.X....XX.X.......X..X....X..X....X..X..#10
...................................X.....X.X.....XXX.......X..X....X.X.....X...X.#11
...................................X.....X.X....XX.X.......X.X.....X...X...X..X..#12
...................................X.....X.X....XX.X.......X..X....X..X....X..X..#13
...................................X.....X.X.....XXX.......X..X....X.X.....X...X.#14

...................................X.....X.X.....XXX.......X..X....X.X.....X...X.
...................................X.....X.X.....XXX.......XX......X..X....X....X
...................................X.....X.X....XX.X.......X..X....X..X....X..X..
...................................X.....X.X....XX.X.......X.X.....X...X...X..X..
...................................X.....X.X....XX.X.......XX......X...X...X...X.


[champagne]

2,078,802 puzzles of the first type, over 26640 "starts", and 1,625,604 puzzles of the 2nd type, over 19672 "starts".

Thanks for the revision.
If I want to go in the direction of a filter for "hard non degenerated tridagons", I'll surely as a first step put mith's file in a "canonical type1/type2" morph, so duplicating your work.
I intend to use as "canonical" the morph with the extra cell in box 9 over the main diagonal

[champagne]

to confuse everyone furthur .. the 14 ED ways for the clues making up the 12 tridagon clues have 5 ED patterns

I'll check your post later to-day, but, in line with the last post, I am expecting 6 ED patterns, 3 for each of the 2 types
EDIT should be 9 patterns, 6 in type1 ; 3 in type2

[champagne]

to confuse everyone furthur .. the 14 ED ways for the clues making up the 12 tridagon clues have 5 ED patterns

Hi coloin,
it's not easy to go from your view to the ED magic squares.
For me the 9 ED solutions are in boxes 8 9

Code: Select all

type 1   
x..  xzz   
.x.  zxz   
..x  zz.   


Only one permutation is valid here, the extra cell can be any of the 6 cells marked 'z'

Code: Select all

type 2
 x.. xzz
 .x. ..z
 ..x ..x

here, we must use one of the 2 permutations giving the 'X' pattern. I take as canonical the pattern with the extra cell over the main diagonal

[coloin]

Im still quite dismayed that there are actually only two "starts" ...
I will repeat the possible placements... still only 8 ED with a ratio of 3:1 of ED patterns for the "starts"

Hidden Text: Show

Code: Select all

..12......2..3....3....1...2.........1...2.....31................................# 1
..12......2..3....3....1...2.........1...3.....31................................# 2
..12......2..3....3....1...2.........1.3.......3.1...............................# 3
..12......2..3....3....1...2.........1.3.......3.2...............................# 4
..12......2..3....3....1...2....3....1.........3.1...............................# 5
..12......2..3....3....1...2....3....1.........3.2...............................# 6
..12......2..3....3....1...2...1.....1...2.....3.................................# 7
..12......2..3....3....1...2...1.....1...3.....3.................................# 8
..12......2..3....3....1...2..1......1.........3..2..............................# 9
..12......2..3....3....1...2..1......1..2......3.................................#10
..12......2..3....3....1...2..3......1.........3..2..............................#11
..12......2..3....3....1...2..3......1..2......3.................................#12
..13......2..1....3....2...2.........1...3.....31................................#13
..13......2..1....3....2...2.........1...3.....32................................#14
..13......2..1....3....2...2.........1..2......3..1..............................#15
..13......2..1....3....2...2.........1..3......3..1..............................#16
..13......2..1....3....2...2....1....1.........3.2...............................#17
..13......2..1....3....2...2....1....1.2.......3.................................#18
..13......2..1....3....2...2....3....1.........3.2...............................#19
..13......2..1....3....2...2....3....1.2.......3.................................#20
..13......2..1....3....2...2...3.....1.........31................................#21
..13......2..1....3....2...2...3.....1.........32................................#22
..13......2..1....3....2...2..1......1..2......3.................................#23
..13......2..1....3....2...2..1......1..3......3.................................#24
                                                                                   
                                                                                   
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.# 1
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.# 2
...................................X.....X.X.....X.X.......XX......X..X....X....X# 3
...................................X.....X.X.....X.X.......XX......X..X....X....X# 4
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.# 5
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.# 6
...................................X.....X.X.....X.X.......XX......X..X....X....X# 7
...................................X.....X.X.....X.X.......XX......X..X....X....X# 8
...................................X.....X.X.....X.X.......XX......X..X....X....X# 9
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#10
...................................X.....X.X.....X.X.......XX......X..X....X....X#11
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#12
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#13
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#14
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#15
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#16
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#17
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#18
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#19
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#20
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#21
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#22
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#23
...................................X.....X.X.....X.X.......X..X....X.X.....X...X.#24



and i was wrong to say

didn't think that the "starts" had anything to do with the guardians.

The guardian cell is always the impossible third location in the diagonal pattern ..... and this is defined ....which is obvious now

[champagne]

last chunk was closed with still plenty of high ratings, but on these as best skfr

Code: Select all

39.7...........7...4.....1..5.87..31...5.68.7....1365..15.38.76..81.7......65.18.;11.3/10.5/8.3
.74.6..1...2..3............1..65..87...8.73.1.8..3165.....85.76...3.61.5.6.17.8..;11.3/11.3/2.6
1.3..85........879.8..........79..549..2.57.8....8492.....27..5..58.94.7...45....;11.3/11.3/2.6
9.4...3....2...6.7...3......5.78..13.8.1.35.6....6587.....17.3....6.81.5...53.76.;11.3/11.3/2.6


may-be coloin will find something of value with a lower skfr
2 more chunks should come this week