T&E(3) Puzzles (split from "hardest sudokus" thread)

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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby totuan » Fri Nov 11, 2022 5:54 pm

denis_berthier wrote:
mith wrote:
Code: Select all
1.3....89.57.8.....68..2....8.....4.......3...34....123....14.....92...3....43..1;15082;482867;3

The first has a relatively tame TOFC from the 6 guardian candidate choice which reduces it to a couple skyscrapers, but the second looks completely disgusting. Curious what your solver will make of this one, Denis.

SER = 11.7
Harder, but solved in W8+OR6W9
..............

hidden-pairs-in-a-column: c5{n1 n3}{r3 r4} ==> r4c5≠9, r4c5≠7, r4c5≠6, r4c5≠5

Code: Select all
 *-----------------------------------------------------------------------------*
 | 1       2-4     3       | 4567    567     567     | 257     8       9       |
 | 24      5       7       | 134     8       9       | 126     236     46      |
 | 9       6       8       | 13457   13      2       | 157     357     457     |
 |-------------------------+-------------------------+-------------------------|
 | 2567    8       12569   | 123     13      567     | 5679    4       567     |
 | 567     129     12569   | 12     #5679    4       | 3      #5679    8       |
 | 567     3       4       | 567     5679    8       |#5679    1       2       |
 |-------------------------+-------------------------+-------------------------|
 | 3       279     2569    | 8       567     1       | 4       25679   567     |
 | 4568    147     156     | 9       2       567     | 5678    567     3       |
 | 2568    279     2569    | 567     4       3       |#256789  25679   1       |
 *-----------------------------------------------------------------------------*

I see that, from here can elimination 4r1c2 as below: Tridagon (567)B5689 => (9)r5c5=(9)r5c8/r69c7=(2)r9c7=(8)r9c7
Present by diagram: => r1c2<>4
Code: Select all
(8)r9c7-r9c1=(8-4)r8c1=(4)r2c1*
 ||
(9)r5c5-r6c5=r6c7--(9=567)r4c679-(567=2)r4c1--(2=4)r2c1*
 ||               |                          |
(9)r5c8/r69c7-----                           |
 ||                                          |
(2)r9c7-r12c7=r2c8---------------------------


Thanks for the puzzle!
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby denis_berthier » Fri Nov 11, 2022 6:59 pm

.
It's a much longer chain.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby mith » Mon Nov 14, 2022 5:46 pm

I've added my results on trivalue oddagons in the second post of the thread.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby denis_berthier » Thu Dec 01, 2022 3:54 am

.
In a previous post (http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1321.html)
I stated that all the puzzles in mith's database of 63,137 T&E(3) min-expands (http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1304.html)
are indeed in T&E(W2, 2).

My recent calculations allow to extend the above results:
all the puzzles in mith's database of 158,276 T&E(3) min-expands (http://forum.enjoysudoku.com/t-e-3-puzzles-split-from-hardest-sudokus-thread-t40514.html)
are indeed in T&E(W2, 2).

And it is enough to prove:
All the known 9x9 sudoku puzzles in T&E(3) are indeed in T&E(W2, 2) or less.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby mith » Fri Dec 23, 2022 9:41 pm

Very nice result, Denis. I wonder if we will find any that go beyond T&E(W2,2).

I've been giving my computer a break from generating puzzles, but I will likely resume work in the new year. jovi_al provided a large list of puzzles generated on the trivalue oddagon pattern which I need to run a depth check on to see if any are depth 3 and need to be added.
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Re: T&E(3) Puzzles (split from "hardest sudokus" thread)

Postby denis_berthier » Wed Dec 28, 2022 9:34 am

mith wrote:Very nice result, Denis. I wonder if we will find any that go beyond T&E(W2,2).

Hi mith. Thanks.
The trivalue oddagon pattern requires more than T&E(W2, 2) to be proven contradictory. Even if it didn't, this wouldn't imply that puzzles with an anti-tridagon are in T&E(W2, 2). Finally, we don't know if all the puzzles in T&E(3) have an extended anti-tridagon.
That makes many reasons for being careful about our expectations.

For more than 10 years, all the known puzzles were at most in T&E(2) - indeed in T&E(B7, 1) = B7B. It was rational at that time to conjecture that all the puzzles were also at most in B7B. With the large number of puzzles in your database, it is now rational to conjecture that all the puzzles are (at most) in T&E(W2,2).

But a conjecture is a conjecture. The longer it lasts, the more interesting it is to find a counter-example.
It's great that my T&E(2) and B7B conjectures were disproved by your Loki puzzle and it's great to see that the new puzzles have led to develop a whole set of new powerful resolution rules (ORk-chains and ORk-g-chains).

I wonder about the other T&E(3) patterns that have been found. Would your techniques allow to develop similar databases concentrated on them?
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