denis_berthier wrote:THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):
That's T&E on top of what set of resolution rules? Sorry, can't easily find the definition of T&E(2).
denis_berthier wrote:THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):
nazaz wrote:denis_berthier wrote:THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):
That's T&E on top of what set of resolution rules? Sorry, can't easily find the definition of T&E(2).
nazaz wrote:That's T&E on top of what set of resolution rules? Sorry, can't easily find the definition of T&E(2).
denis_berthier wrote:.
One may be interested in the resolution states after T&E(2) has been applied to these two puzzles:
For ........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
- Code: Select all
Resolution state after T&E(2):
+----------------+----------------+----------------+
! 3 256 478 ! 459 4579 4589 ! 27 68 1 !
! 145 456 458 ! 156 47 2 ! 39 678 39 !
! 19 269 79 ! 16 3 18 ! 278 4 5 !
+----------------+----------------+----------------+
! 8 459 6 ! 23 459 14 ! 4579 1237 237 !
! 459 7 1 ! 23 8 459 ! 3459 235 6 !
! 2 3 459 ! 1459 6 7 ! 459 19 8 !
+----------------+----------------+----------------+
! 459 8 2 ! 7 459 6 ! 1 359 34 !
! 6 1 459 ! 459 2 3 ! 58 5789 47 !
! 7 459 3 ! 8 1 459 ! 6 259 249 !
+----------------+----------------+----------------+
141 candidates
For ........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2
- Code: Select all
Resolution state after T&E(2):
+----------------+----------------+----------------+
! 3 467 258 ! 459 4579 4569 ! 27 68 1 !
! 145 456 458 ! 158 47 2 ! 39 678 39 !
! 19 79 289 ! 18 3 16 ! 267 4 5 !
+----------------+----------------+----------------+
! 8 459 1 ! 459 2 3 ! 56 5679 47 !
! 459 2 6 ! 7 459 8 ! 1 359 34 !
! 7 3 459 ! 6 1 459 ! 8 259 249 !
+----------------+----------------+----------------+
! 459 1 7 ! 23 6 459 ! 3459 235 8 !
! 6 8 459 ! 23 459 14 ! 4579 1237 237 !
! 2 459 3 ! 1459 8 7 ! 459 19 6 !
+----------------+----------------+----------------+
141 candidates
denis_berthier wrote:.
Here is probably the breakthrough of the year in Sudoku.
THE FOLLOWING TWO PUZZLES FOUND BY MITH ARE NOT IN T&E(2):
- Code: Select all
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2
999_Springs wrote:these two pencilmark grids are isomorphic. starting from the first one, swap digits 6 and 8, rows 4 and 5, rows 7 and 8, bands 2 and 3, and columns 2 and 3, and you get the second one. so when it comes to solving them, they are exactly the same puzzle except for different hidden singles at the start. i would consider these as one puzzle and not two different ones
champagne wrote:nazaz wrote:That's T&E on top of what set of resolution rules? Sorry, can't easily find the definition of T&E(2).
As you, I don't know what is T&E(2), but here, the key point is the exotic pattern ("Thor's Hammer") used by mith as "seed".
Easy to spot, this pattern is still perfectly seen if the last posts of "Denis". This means that this pattern resists to the T&E(2), whatever is the content of it.
The very high rating in Sudoku Explainer shows also that the pattern is highly resistant to the classical chains and "chain nets" approach.
A true breakthrough in the list of exotic patterns.
This is good for the challenge of the highest SE rating. As for some previous exotic patterns as a double JE, it discards such grids from the challenge of the "hardest puzzle". (in fact, I think that most of the grids having an identified "exotic pattern" are discarded from the "hardest grid challenge").
999_Springs wrote:these two pencilmark grids are isomorphic. starting from the first one, swap digits 6 and 8, rows 4 and 5, rows 7 and 8, bands 2 and 3, and columns 2 and 3, and you get the second one. so when it comes to solving them, they are exactly the same puzzle except for different hidden singles at the start. i would consider these as one puzzle and not two different ones
........1.....2.......3..45..6.......71.8....23..67..8.827..1..6...23...7.381.6.. ED=11.9/1.2/1.2
........1.....2.......3..45..1.23....267.81..73.61.8...17.6.....8.......2.3.87..6 ED=11.8/1.2/1.2
........1.....2.34..2.3156.....5......4...6...78..6.......651..1..2.43..4..3...25 ED=11.8/1.2/1.2
........1.....2.34..2.3156.....5......4...6...78..6.......65.4.1..2.43..4..31..25 ED=11.8/1.2/1.2
57....9..........8.1.........168..4......28.9..2.9416.....2.....6.9.82.4...41.6.. ED=11.9/1.2/1.2 "Loki"
mith wrote:Indeed, these are two of the minimals from the 30c morph-dependent 11.9. The singles only get them to 29c though, whereas the other two minimals get back to 30c (and this is presumably why they are in T&E(2) - that 30th digit in the others takes at least two 11.8 steps, it's not trivial!)
denis_berthier wrote:mith wrote:Indeed, these are two of the minimals from the 30c morph-dependent 11.9. The singles only get them to 29c though, whereas the other two minimals get back to 30c (and this is presumably why they are in T&E(2) - that 30th digit in the others takes at least two 11.8 steps, it's not trivial!)
Applying isomorphisms or Singles can't change the T&E(n) classification of a puzzle.
mith wrote:denis_berthier wrote:mith wrote:Indeed, these are two of the minimals from the 30c morph-dependent 11.9. The singles only get them to 29c though, whereas the other two minimals get back to 30c (and this is presumably why they are in T&E(2) - that 30th digit in the others takes at least two 11.8 steps, it's not trivial!)
Applying isomorphisms or Singles can't change the T&E(n) classification of a puzzle.
I understand that. The point is that the two puzzles you mentioned are morphs of each other after singles, but the other two puzzles *aren't* - they have an extra digit. All four are minimals of the same 30c puzzle, but the first two only get to 29c with singles - that 30th digit is the difference.
All four can be made 11.9 with the right morph, but only the first two are not in T&E(2).
mith wrote:Wow, that is very much an unexpected result, Denis.