The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections

Postby JPF » Mon May 19, 2008 11:51 pm

tarek wrote:
ronk wrote:while obtaining maximal symmetry ....
maximal symmetry for asymmetrical puzzles is also something worthwhile trying. I know that it was duscussed in another thread. I couldn't remeber an algorithm surfacing from the discussions though.

See here.

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Postby tarek » Tue May 20, 2008 8:16 am

Thanx JPF, I looked at the algorithms (including one by me:( ).

There is a small problem ....

Puzzle P has 20 clues in line format you can refer to each clue as C(1) ...C(21)
Let's take an isomorph Q(2) for instance.... (range is 2*6^8)

No Symmetry modulo 0
No symmetry modulo 1
Q(2):-C(14)-C(C18) will achive symmetry (modulo2)

I assume then that your algorithm goes through ALL plug out /plug in clues to achive this. this will be easy for small modulo but when it is big then the search will take ages.

Is that what you've experienced JPF ?

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Postby coloin » Tue May 20, 2008 1:47 pm

Tricky one to sort out.

gsf had a relevant coment here

When I manipulated the puzzles there are always several options - I was trying to manipulate the puzzle to closly resemble the morphed GN puzzle.
I had to decide whether to go for a pattern match up - or a clue matchup.

I may have matched 15 clues - although there were 16 clues matching - at the expence of the pattern - which is the more important aspect.

Here is the puzzle with four singles clues initially. This has an effect on the -q1 and -q2 rating. But the massive sx9/sxt wil potentially give champagne's program a challenge - perhaps not !

Code: Select all
+---+---+---+
|1..|...|...|
|.2.|4..|.6.|
|..3|...|5.1|
+---+---+---+
|.4.|.86|...|
|...|.49|.8.|
|...|2..|...|
+---+---+---+
|5.7|...|3..|
|.6.|9..|.4.|
|...|...|..7|
+---+---+---+   Cloudy Bay

1.........2.4...6...3...5.1.4..86.......49.8....2.....5.7...3...6.9...4.........7

ER 10.9

sx9 # 3941
sxt # 2378

-q1 # 71324 FNP C21.m/M2.4.8200
-q2 # 44674 FNBP C21.m/M2.4.8200

C
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Postby champagne » Tue May 20, 2008 2:08 pm

coloin wrote:Here is the puzzle with four singles clues initially. This has an effect on the -q1 and -q2 rating. But the massive sx9/sxt wil potentially give champagne's program a challenge - perhaps not !
|5.7|...|3..|
|.6.|9..|.4.|
|...|...|..7|
+---+---+---+ Cloudy Bay

1.........2.4...6...3...5.1.4..86.......49.8....2.....5.7...3...6.9...4.........7

ER 10.9

sx9 # 3941
sxt # 2378

-q1 # 71324 FNP C21.m/M2.4.8200
-q2 # 44674 FNBP C21.m/M2.4.8200[/code]
C


Solvable at level 3, but in 17 seconds.
Using level 4, the SK loop comes immediatly and the puzzle is solved in 7 seconds.

Just to compare,
silver plate has been solved in 127 seconds with a printsize of 650K
Cloudy Bay
- 7 seconds and 61K forcing level 4 and SK loop cleaning
- 17 seconds and 130K at level 3 which likely reflects the potential structural difficutty
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Postby ronk » Tue May 20, 2008 2:37 pm

champagne wrote:Using level 4, the SK loop comes immediatly ...

I don't see an SK loop. Please identify it (but perhaps in another thread).
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Hard?

Postby Papy » Tue May 20, 2008 3:57 pm

Code: Select all
3___9___7_2_____5___7___8_____3_4___1___6___3___7_2_____4___2___8_____4_9___3___1

Easy?

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Postby tarek » Tue May 20, 2008 4:00 pm

coloin wrote:
Code: Select all
+---+---+---+
|1..|...|...|
|.2.|4..|.6.|
|..3|...|5.1|
+---+---+---+
|.4.|.86|...|
|...|.49|.8.|
|...|2..|...|
+---+---+---+
|5.7|...|3..|
|.6.|9..|.4.|
|...|...|..7|
+---+---+---+   Cloudy Bay
swapping r5 with r6 then c4 with c5 will give you a 180 Clear horizon:D

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Postby coloin » Tue May 20, 2008 4:20 pm

Indeed I missed the Box 5 symmetry, I too dont see the SK loop.
Papy
This format is better for most

Code: Select all
3...9...7.2.....5...7...8.....3.4...1...6...3...7.2.....4...2...8.....4.9...3...1

+---+---+---+
|3..|.9.|..7|
|.2.|...|.5.|
|..7|...|8..|
+---+---+---+
|...|3.4|...|
|1..|.6.|..3|
|...|7.2|...|
+---+---+---+
|..4|...|2..|
|.8.|...|.4.|
|9..|.3.|..1|
+---+---+---+

Ease of solving is subjective....except these programs give it a rating
-q1 gives it # 608 FNP C21.M/S8.f/M1.3.21
sx9/sxt gives it # 142/ 93

C
Last edited by coloin on Tue May 20, 2008 12:52 pm, edited 1 time in total.
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Re: Hard?

Postby tarek » Tue May 20, 2008 4:21 pm

Papy wrote:
Code: Select all
3___9___7_2_____5___7___8_____3_4___1___6___3___7_2_____4___2___8_____4_9___3___1

Easy?
will not challenge the hardest (Not even close).... This puzzle will make many NICE people very happy:idea:

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Postby champagne » Tue May 20, 2008 5:14 pm

ronk wrote:
champagne wrote:Using level 4, the SK loop comes immediatly ...

I don't see an SK loop. Please identify it (but perhaps in another thread).


here the start of the solver


1 r3c1=4 r7c6=4 r1c3=6 r9c3=4

Code: Select all
1     5789   6    |3578  23579  23578   |24a789 2379   234A89
789   2      589  |4     13579  13578   |789    6      389   
4     789    3    |678   2679   278     |5      279    1     
---------------------------------------------------------------
2379  4      1259 |1357  8      6       |1279   123579 2359   
2367  1357   125  |1357  4      9       |1267   8      2356   
36789 135789 1589 |2     1357   1357    |14679  13579  34569
---------------------------------------------------------------
5     189    7    |168   126    4       |3      129    2689 
238   6      128  |9     12357  123578  |128    4      258   
2389  1389   4    |13568 12356  12358   |12689  1259   7     


In that map, we have a typical SK loop (at least for me), exactly in the place where it stays normally. It is not a pattern with 3 candidates per cell, but it is a SK loop.
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Postby tarek » Wed May 21, 2008 11:52 am

In the abscence of any other freely downloadable puzzle pattern canonicalizer .....

Are there any ideas of how to present puzzles (especially the ones that closely follow the diagonal patterns), or should we just carry on with what we were doing ?

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Postby gsf » Wed May 21, 2008 12:18 pm

tarek wrote:In the abscence of any other freely downloadable puzzle pattern canonicalizer .....

Are there any ideas of how to present puzzles (especially the ones that closely follow the diagonal patterns), or should we just carry on with what we were doing ?

I'm looking at my symmetrize routine to allow for errors
so that it will determine the closest symmetry via a distance measure
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Postby tarek » Wed May 21, 2008 12:34 pm

gsf wrote:I'm looking at my symmetrize routine to allow for errors
so that it will determine the closest symmetry via a distance measure
that would be great, I'm assuming that it should give consistant results for 100 isomorphs of the same puzzle as a test.

I've just posted my idea for an algorithm on the Best symmetry thread.

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Postby gsf » Wed May 21, 2008 3:21 pm

moved to The Best Symmetry thread
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Re: Hard?

Postby m_b_metcalf » Wed May 21, 2008 6:03 pm

Papy wrote:
Code: Select all
3___9___7_2_____5___7___8_____3_4___1___6___3___7_2_____4___2___8_____4_9___3___1

Easy?

Here's what Sudoku Explainer says about it:
Code: Select all
Analyzing Sudoku #1
58 Hidden Single
1 Direct Hidden Pair
3 Pointing
1 X-Wing
2 Hidden Pair
1 Unique Rectangle type 1
1 Turbot Fish
1 Forcing X-Chain
7 Forcing Chain
4 Region Forcing Chains
2 Cell Forcing Chains
Hardest technique: Cell Forcing Chains
Difficulty: 8.5

Please note that it's not minimal -- r4c4 is redundant. Here's a modified minimal version:
Code: Select all
 7 . . . 2 . . . 1
 . 3 . . . . . 4 .
 . . 6 . . . 5 . .
 . . . 6 . 9 . . .
 1 . . . 7 . . . 9
 . . . 5 . 4 . . .
 . . 4 . . . 2 . .
 . 5 . . . . . 8 .
 9 . . . 3 . . . 7

Analyzing Sudoku #1
54 Hidden Single
2 Direct Hidden Pair
2 Naked Single
11 Pointing
1 Claiming
4 Naked Pair
1 X-Wing
2 Hidden Pair
1 Naked Triplet
2 Swordfish
1 XY-Wing
3 Bidirectional Y-Cycle
1 Turbot Fish
14 Forcing Chain
9 Region Forcing Chains
3 Cell Forcing Chains
7 Dynamic Cell Forcing Chains
2 Dynamic Contradiction Forcing Chains
2 Dynamic Double Forcing Chains
1 Dynamic Region Forcing Chains
Hardest technique: Dynamic Cell Forcing Chains
Difficulty: 9.0


Regards,

Mike Metcalf
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