## The hardest sudokus

Everything about Sudoku that doesn't fit in one of the other sections
champagne wrote:1) T&E is often order dependent that's right. Counting possible solutions of a puzzle is not. So the time I gave is not order dependant.

2) Is counting of solutions a kind of rating ? I would say yes and no. It follows all move possibilities and processing time is one acceptable way to measure the work done doing that .
Why not?
I can accept without any problem that a rating intend to classify puzzles and to identify specific properties. This gives added value for sure.

I'm not sure what you mean by counting possible solutions
if you count using singles only you will get different results than with the kitchen sink
change the kitchen sink order and you will get different results again

counting is trikcy because all of our coding is inherently ordered
as soon as we write for i in ... we are sunk without some careful and extra consideration
for example, when method M finds an elimination, does it apply the elimination immediately
so that the remainder of method M benefits from that elimination?
if so, how would the counts differ on a permutation of the input puzzle?
when method M finds an elimination does it restart at the beginning of the method order or does it continue with method M?
gsf
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Location: NJ USA

gsf wrote:you can use my solver to play with e.g. the recalcitrant candidates in easter monster

I had realized this...but wasnt sure how high to raise the bar, or code it .

Not sure what it would mean either - although I think easier puzzles will turn out to have a number of these pairs........depends on the level .

Your M3 constraint limit is perhaps too easy ?

I think SE maybe has not taken the next logical step

I can solve the 9.3 - my nephew could do the first placement , but I cant anticipate what the effect on ratings will be..... !

C
coloin

Posts: 1733
Joined: 05 May 2005

Hi coloin,

I had a look on your puzzle. He is rated 31 2s906 on my side, a puzzle in the lowest part of "hardest puzzles".

Your loci is on a stuff my solver does not use, so I could not directly check whether he could do similar analysis.

If the solver works normally, the sequence is:

#8r1c6
#3r1c2
#1r1c8 ;1r2c5
#1r8c5 ;1r9c2
#6r9c5(UR)
#4r2c7 4r89c9
#2r2c5 2r3c2
#6r1c2 6r2c5
#9r8c2
#8r2c5

1 r2c9=4
2 r4c3=1
3 r5c8=1
4 r8c2=1
5 r2c7=1
6 r4c1=3
7 r4c7=6

As you can see, your loci is not in the field of what can be accessed easily in my non T&E process.

This is something I often check when I try to find equivalence between a T&E approach and what comes out of my solver.
Without any doubt, T&E offers wider possibilities. When I started using tagging,I studied MEDUSA. Many of the puzzles solved by Bob Hansom thru forcing chains remained unsolved (tagging level one is very close to MEDUSA and for me, forcing chains belong to the T&E family).

I made a second test forcing the solver to work at level 4, studying pairs to see whether some AC2 would give a quick elimination of all possibilities but one.
Again, nothing came.
champagne
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Location: France Brittany

Champagne - thanks for following that one up,.....almost certainly the pair loci of clues were not the only with that property in the 9.3 puzzle.

gsf - your example does explain your output, in particular it shows the iterations for a specific P1. - The P1 is picked because of its bivalue properties.

Code: Select all
`SE doesn't combine the results of its paired (double proposition) failures`
probably just as well !

Is it possible to give a value to a "puzzle" with a double preposition failure - ie the level of technique required to propagate the contradiction/constraint ?

C
coloin

Posts: 1733
Joined: 05 May 2005

coloin wrote:Is it possible to give a value to a "puzzle" with a double preposition failure - ie the level of technique required to propagate the contradiction/constraint ?

paired (nesting 2) propositions only propagate the constraints in scope
the hardest require FNB (singles + locked candidates) and are labeled V3
there are 26 in the q1 hardest catalog
the rest of the hardest, golden nugget included, require FN and are labeled V2
there are 8079 in the q1 hardest catalog

you can have different constraints for normal and propositions
Code: Select all
`-q'+P*(FNB)'`

uses FNB for propositions and all constraint methods otherwise
gsf
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Location: NJ USA

### Hardest Sudokus according to solver programs:

I thought that the list of hardest puzzles needed an update, this is the list as far as I recall. This is also a call for contributions/corrections

Hardest Sudokus according to various solver programs:

Openly accessible solver Programs:

Code: Select all
`Rating Program: gsf's sudoku q1 (rating)Rating: 99408Poster: JPFLabel: Easter Monster1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1 1 . . | . . . | . . 2   . 9 . | 4 . . | . 5 .   . . 6 | . . . | 7 . .  -------+-------+------  . 5 . | 9 . 3 | . . .   . . . | . 7 . | . . .   . . . | 8 5 . | . 4 .  -------+-------+------  7 . . | . . . | 6 . .   . 3 . | . . 9 | . 8 .   . . 2 | . . . | . . 1  Rating Program: gsf's sudoku q1 (Processing time)Rating: 4m19s@2Ghz Poster: tarekLabel: tarek071223170000-052..1..4.......6.3.5...9.....8.....7.3.......285...7.6..3...8...6..92......4...1... . . 1 | . . 4 | . . .   . . . | . 6 . | 3 . 5   . . . | 9 . . | . . .  -------+-------+------  8 . . | . . . | 7 . 3   . . . | . . . | . 2 8   5 . . | . 7 . | 6 . .  -------+-------+------  3 . . | . 8 . | . . 6   . . 9 | 2 . . | . . .   . 4 . | . . 1 | . . .  Rating Program: Nicolas Juillerat's Sudoku explainer 1.2.1Rating: 11.9 Poster: tarekLabel: golden nugget.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... . . . | . . . | . 3 9   . . . | . . 1 | . . 5   . . 3 | . 5 . | 8 . .  -------+-------+------  . . 8 | . 9 . | . . 6   . 7 . | . . 2 | . . .   1 . . | 4 . . | . . .  -------+-------+------  . . 9 | . 8 . | . 5 .   . 2 . | . . . | 6 . .   4 . . | 7 . . | . . .  Rating Program: dukuso's suexrat9Rating: 4483coloincol-02-08-071 .2.4.37.........32........4.4.2...7.8...5.........1...5.....9...3.9....7..1..86.. . 2 . | 4 . 3 | 7 . .   . . . | . . . | . 3 2   . . . | . . . | . . 4  -------+-------+------  . 4 . | 2 . . | . 7 .   8 . . | . 5 . | . . .   . . . | . . 1 | . . .  -------+-------+------  5 . . | . . . | 9 . .   . 3 . | 9 . . | . . 7   . . 1 | . . 8 | 6 . .  Rating Program: dukuso's suexratt (10000 2 option)Rating: 2141 Poster: tarekLabel: golden nugget.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... . . . | . . . | . 3 9   . . . | . . 1 | . . 5   . . 3 | . 5 . | 8 . .  -------+-------+------  . . 8 | . 9 . | . . 6   . 7 . | . . 2 | . . .   1 . . | 4 . . | . . .  -------+-------+------  . . 9 | . 8 . | . 5 .   . 2 . | . . . | 6 . .   4 . . | 7 . . | . . .  `

Other solver programs:
Code: Select all
`Rating Program: Ravel's solver (RMS)Rating: 24 stepsPoster: OceanLabel: Ocean's New Year's present for RW  .....1.2.3...4.5.....6....7..2.....1.8..9..3.4.....8..5....2....9..3.4....67.....  . . . | . . 1 | . 2 .   3 . . | . 4 . | 5 . .   . . . | 6 . . | . . 7  -------+-------+------  . . 2 | . . . | . . 1   . 8 . | . 9 . | . 3 .   4 . . | . . . | 8 . .  -------+-------+------  5 . . | . . 2 | . . .   . 9 . | . 3 . | 4 . .   . . 6 | 7 . . | . . .  Rating Program: Obi-Wahn's solverRating: 1 Star - 7 Jellies - 27 SwordsPoster: coloinLabel: coloin-04/13-1414  1.......2.9.4...5...6...7...5.3.4.......6........58.4...2...6...3...9.8.7.......1 1 . . | . . . | . . 2   . 9 . | 4 . . | . 5 .   . . 6 | . . . | 7 . .  -------+-------+------  . 5 . | 3 . 4 | . . .   . . . | . 6 . | . . .   . . . | . 5 8 | . 4 .  -------+-------+------  . . 2 | . . . | 6 . .   . 3 . | . . 9 | . 8 .   7 . . | . . . | . . 1  Rating Program: Champagne's solver (Processing time)Rating: 96s250Poster: tarekLabel: golden nugget.......39.....1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2....6..4..7..... . . . | . . . | . 3 9   . . . | . . 1 | . . 5   . . 3 | . 5 . | 8 . .  -------+-------+------  . . 8 | . 9 . | . . 6   . 7 . | . . 2 | . . .   1 . . | 4 . . | . . .  -------+-------+------  . . 9 | . 8 . | . 5 .   . 2 . | . . . | 6 . .   4 . . | 7 . . | . . .  `

tarek
Last edited by tarek on Mon Apr 14, 2008 1:29 pm, edited 2 times in total.

tarek

Posts: 2698
Joined: 05 January 2006

At the risk of starting a row, a few interesting words on the subject !!
denis_berthier wrote:T&E is a whole family of algorithms (see the "concept of a resolution rule" thread), depending on which set of rules is used to prune the search.
AFAIK, SE uses T&E pruned by a lot of logic rules.
I think Champagne's algorithm works the same way: breadth-first search (instead of the usual depth-first) pruned by a lot of logic rules, with the assumptive part disguised under tagging, layers, fusion of layers, choice and all the algorithmic glue.

In this context, the rate of a puzzle is highly dependent on the rules used to prune the search. Based on Ruud's top 10,000, I've shown that nrczt rules completely change the rating landscape.
The most stupid rating would certainly be the computation time of an algorithm, especially one relying on massive T&E or tagging, for which humans and computers do not perform the same way. SE is smarter than this, as its ratings rely on the most complex rule needed to solve the puzzle. But, for levels where logic rules are not enough and some form of T&E is used, the rating is very unclear to me. Indeed, I don't understand at all what "dynamic forcing chain" means.
I'd like to know just what the difference is between 11.0 and 11.8 too.

If SE rates the length of the chains [?] - which is an assumptive technique, but it ignores the double proposiution pairs......which is also an assumptive technique.......
gsf wrote:because SE doesn't combine the results of its paired (double proposition) failures
myself wrote: We are indeed trying to rate the puzzles, you need to solve them first and then decide how difficult that was.

We can solve nearly all puzzles with double proposition pairs....fairly easily [not EM though]
How can we numerate how difficult it is.

? number of double proposition successes/failures at medium level - out of total.
? number of triple proposition successes/failures at low level - out of total

In an easy puzzle the only successes will be the correct clues - all other proposition clues will fail.

Thge ratio of successes/failure is higher in a harder puzzzle.

As you get a harder puzzle, there will be more "successes" with incorrect clues - depending on the level set for extending the solving path leading to an eventual constraint [failure]......
C
coloin

Posts: 1733
Joined: 05 May 2005

coloin wrote:We can solve nearly all puzzles with double proposition pairs....fairly easily [not EM though]

we can solve all known hardest puzzles with proposition pairs -- some may just require stronger constraints in scope
all of the hardest solve with
Code: Select all
`-X -q'FNP*(FNBT2H2)-G'`

-X: only use contradictions discovered by propositions (ignore stumbled upon solutions)
FN: singles
P*: paired propositions (nesting 2 in the -v2 trace)
(FNBT2H2): paired propositions propagate FNBT2H2 constraints (naked/hidden-singles locked-candidates naked/hidden-pairs)
-G: no backtrack guessing (besides the propositions themselves, which are guessing and brute force)

I went back to the q1 taxonomy to verify these statements and an interesting patrtitioning fell out

almost all solved with
Code: Select all
`-X -q'FNP*(FN)-G'`

easter monster class solves with
Code: Select all
`-X -q'FNP*(FNB)-G'`

and, what escaped analysis before
golden nugget class solves with
Code: Select all
`-X -q'FNP*(FNBT2H2)-G'`

the difference is I hadn't used -X (to ignore proposition solutions) before
so golden nuggent is harder than eastern monster when only paired proposition contradictions are considered
throw in paired proposition solutions and golden nugget yields to easier proposition constraints (FN)
but easter monster still required (FNB)

here are the 3 golden nugget class puzzles that require
Code: Select all
`-X -q'FNP*(FNBT2H2)-G'`

#!sudoku -c4,Q1,ER,XR,puzzle,label,Q1time,ERtime,Q1stats,stats
95649,115,3792,000000039000001005003050800008090006070002000100400000009080050020000600400700000,Golden-Nugget,4.00s,0,C21.m/F51657.79394/N183416.334233/P1.2.137135.4.0.334061.22.5.2.236/M2.1.164025/V2,C21.m/F302.1099/N168.599/B67.160.103.57/T35.117.39.5/H23.46.23.1/X45.108/Y2.24/K1.3.21.0.0.0.0.2.1/O11.20/G181.0.10/M2.679.9
75782,113,1968,100000002030400050006000700080509000000070000000830040700000600050008090002000001,jpf-04/05,1.00s,0,C21.m/F12752.22424/N47412.97432/P1.5.26947.4.1.75767.19.3.2.238/M2.6.31697/V2,C21.m/F9.45/N5.10/B8.19.19/T4.7.3.1/H3.6.3/W1.3.2/X1.1/Y3.15/K3.10.26.0.0.1.7.0.1.1/O3.3/G7.0.1/M1.3.29
60691,114,1905,600000002090400050001000700050084000000020000000305040200000600030009080007000001,coloin-04-10,1.00s,10h58m,C21.m/F10982.17906/N38024.77245/P1.3.20985.3.1.60675.22.3.2.237/M2.1.505197/V2,C21.m/F8.42/N17.22/B10.34.34/H6.12.6/Y2.5/K4.15.23.0.2.2.7.3.1/O3.6/G23.0.1/M1.5.7
gsf
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Joined: 21 September 2005
Location: NJ USA

gsf wrote:
Code: Select all
`-X -q'FNP*(FNBT2H2)-G'`

I can smell some fresh lists coming very soon

from my end I'll post only puzzles in my database that haven't been posted before.

tarek

tarek

Posts: 2698
Joined: 05 January 2006

Tarek is calling for contribution.

As I am not producing puzzles, my contribution will be an update of all puzzles I studied.

This is done with the last version of the solver, including mainly vicinity analysis and a better handling of cross steps memory for couple tags;
Golden Nugget remains at the top of the list, but Ocean new year number 2 is very close.
The last two given by gsf are far below. Ocean new year number 1 is easier to solve.
As soon as I'll have time, I will analyse the second puzzle to try to catch why it was so difficult to solve.
This has be done without forcing level 4, but I am not expecting signifcant changes doing it.

Code: Select all
`000000039000001005003050800008090006070002000100400000009080050020000600400700000 Golden Nugget 120s >187  96s250000001020300040500000600007001000006040080090500000300800002000050090400006700000 Ocean's New Year's  #2 > 47  94s953800000004000090030001400700060305000002000000000069050007000100020030090400000008 tarek-031##95209#2331#1211 >250  78s922800003000070060090004500000002000004030001070500000800000009001060070030000200500 dml4 >47  56s594000001020300040500000600007002000001080090030400000800500002000090030400006700000 Ocean's New Year's >63  30s172`

I forgot that one

Code: Select all
`300000002080070010006900000050704000000000008000510070009000300010040080200000006 tarek 005##99072#2511#1537  156  92s406`

subject to checking because I run the batch doing something else.

It will stay anyway in the top list
champagne
2017 Supporter

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Joined: 02 August 2007
Location: France Brittany

Code: Select all
`600000002090400050001000700050084000000020000000305040200000600030009080007000001,coloin-04-10is actually6.......2.9.4...5...1...7...5..84.......2.......3.5.4.2.....6...3...9.8...7.....1,coloin-4/13-1600 `

In the top 3 AFAIK in Obi-Whan's solver.

What is 'exact' command to filter for "v3" puzzles and those in GN"class"

Heres my contribution !

Here are the top scoring in catagory - puzzles which I generated some time ago.
All new, purged from taxonomy and also those puzzles not in taxonomy.

classified into M3,M2,suexrat9,suexratt.

-q1-M3 puzzles
.2.4..7.........2......7.94.9.3...7...8.5.3.......1.....5..86...4.9....71........ # 97870 # col-02-08-001
.2.4..7....6....2........4..9.3...7......53....8.1.9....5...6...6.9....71....8... # 97684 # col-02-08-002
.2.4..7..........2.......43.9.2...7...8.5.........1...5....69...3.9....7..1..86.. # 97668 # col-02-08-003
.2.4..7.......3.29........4.4.2...7.8....1.......5....5....83...6.9....7..1...6.. # 97548 # col-02-08-004
.2.4..7.........34........2.9.3...7.6....5.....8..1.........6...3.9....75.1..89.. # 97532 # col-02-08-005
.2.4..7.........2...6....49.9.3...7.....5.3....8..16....5..8....4.9....71........ # 97517 # col-02-08-006
.9.4..7.......3.29........4.4.2...7.8....1.......5....5.....3...6.9....7..1..86.. # 97212 # col-02-08-007
.2.4..7.........2...6....94.9.3...7.....853......1.6....5.......3.2....7..1..8... # 96974 # col-02-08-008
.2.4..7..7......2........94.9.3...7.....5.3..8....1.....5..86...4.9....71........ # 96867 # col-02-08-009
.3.4..7.........32.......4..9.2...7.8.6..5........19..5....8....2.9....7..1...6.. # 96682 # col-02-08-010
.2.4.....7......2......7.94.9.3...7.....5.3..8....1.....5..86...4.9....71........ # 96448 # col-02-08-011
.2.9..7......4...2.......94.9.3...7......53....8..1.....5...6...6.2....71....8... # 96307 # col-02-08-012
.2.4..7....9....24.......9..9.3...7...8..53......1......5..86...4.2....71........ # 96271 # col-02-08-013
.2.4..7....6....24.......9..9.3...7.....853......1.6....5.......3.2....7..1..8... # 96260 # col-02-08-014
.9.4..7.........29.......43.4.2...7.....5....8....13..5....8....6.9....7..1...6.. # 96248 # col-02-08-015
.2.4..7.........2......7.94.9.3...7.....5.3..8....1.....5..86...4.9....71........ # 96184 # col-02-08-016
.2.4..7....6....24.......9..9.3...7...8..53......1......5...6...4.2....71...8.... # 96115 # col-02-08-017
.2.4..7.........2........94.9.6...7.....5.3....8..1.....5..86...4.9....71...3.... # 96054 # col-02-08-018
.2.9..........7..4..7....92.9.3...7......53....8.1......5...6...4.2....31....8... # 95852 # col-02-08-019
.2.4..79........24..........9.3...7...895.3.......1.....5..86...4.2....71........ # 95795 # col-02-08-020
.2.4..7..........4.......32.9.2...7.6....5.....8..1.........6...3.9....75.1..89.. # 95794 # col-02-08-021
.2.4..7.........2......7.94.9.3...7.....5.3....8..1.....5..86...4.9....71........ # 95638 # col-02-08-022
.2.4..7.......3.29........4.4.2...7...8..1.......5....5.....3...6.9....7..1..86.. # 95629 # col-02-08-023
.2.4....97......2......7..4.9.3...7......13....8.5.6....5..8....4.2....71........ # 95606 # col-02-08-024
.3.4..7.........24.......93.9.2...7.6....5.....8..1.....5...6...2.3....71....8... # 95565 # col-02-08-025
.2.4..7.........2.....2...4.9.3...7......53....8..19....5..86...4.9....7..1...... # 95545 # col-02-08-026
1....6..2.3.4...9....7.5.....85..7...4.........5..48.....6.7....2.....1.9.......3 # 95543 # col-02-08-027

-q1-M2puzzles
.2.9..7..........4..7....92.9.3...7......53....8.1......5...6...4.2....31....8... # 98192 # col-02-08-028
.2.3..7..........2.......34.9.2...7.....5....8....1...7.5...9...6.4....71....86.. # 97597 # col-02-08-029
.2.9..........7..4..7....92.9.3...7......53....8.1......5..86...4.2....71........ # 96863 # col-02-08-030
.2.4..79........2.........4.9.3...7...7..53..8....1.....5.......3.9....71....86.. # 96802 # col-02-08-031
.2.4..7......6..2........94.9.3...7...8.5.3.......1.....5..86...4.2....71........ # 96801 # col-02-08-032
.2.4..7.........92....2...4.9.3...7......53....8..1.....5..86...4.9....71........ # 96780 # col-02-08-033
.3.4..7.........29....7..4..4.2...7.....5....8....13..5....8....6.9....7..1...6.. # 96772 # col-02-08-034
.3.4..7.........24....2..9..9.3...7.6.....3....8..1.......6.5...4.9....71....8... # 96697 # col-02-08-035
.2.4..79........2.........4.9.3.....7....53....87.1.....5..86...3.9....71........ # 96681 # col-02-08-036
.2.4..7.......6.24.......9..9.3...7.5.....3....8..1.....5..86...4.9....7..1...... # 96591 # col-02-08-037
.2.4..7.........2......7.94.9.3...7......53....8..1.....5..86...4.9....71........ # 96519 # col-02-08-038
.2.4..7.........2......6.94.9.3...7...1..5.....8...3....5...6...3.9....71....8... # 96513 # col-02-08-039
.2.4..79.........4..9.....2.9.3...7...8.5.3.......1.....5..86...3.2....71........ # 96478 # col-02-08-040
.2.4.....7......2......7.94.9.3...7.....5.3....8..1.....5..86...4.9....71........ # 96441 # col-02-08-041
.3.4..7.........32.......4..9.2...7.8.6..5........19....5..8....2.9....71.....6.. # 96338 # col-02-08-042
.2.4..7.........2........94.9.3...7.6....53....8.1......5...6...4.2....71....8... # 96306 # col-02-08-043
.2.4..79........2.........4.9.3...7.7....53....8..1.....5..86...3.9....71........ # 96279 # col-02-08-044
.2.4..7.........9...6....42.9.3...7.....5.3....8..16....5..8....4.9....71........ # 96256 # col-02-08-045
.2.4..7....6.....4.......92.9.3...7...8..53......1.6....5.......4.2....71....8... # 96072 # col-02-08-046
.2.4..79.........4.......2..9.3...7...895.3.......1.....5..86...4.2....71........ # 96071 # col-02-08-047
.2.4..7.......3.2........94.9.3...7.....5.3....8..1.....5..86...4.2....7..1...... # 96042 # col-02-08-048
.2.4..7.........2........94.9.3...7...8.5.3.......16....5..8....469....71........ # 95983 # col-02-08-049
.2.4..7.9.......24..........9.3...7...8..53..3....1.....5...6...4.2....71....8... # 95981 # col-02-08-050
.2.4..7.......3.29........4.4.6...7.8....1.......5....5.....3...6.9....7..1..86.. # 95979 # col-02-08-051
1..9....2.3.....4....5.6.....5...7..9...8......6..289....7.9....2.....3.4.......1 # 95936 # col-02-08-052
.2.4..7....6....24.......9..9.3...7...8..53......1.6....5.......4.2....71....8... # 95901 # col-02-08-053
.2.4..7.........34........2.9.2...7...6..5.....8..1...5.....6...3.9....7..1..89.. # 95816 # col-02-08-054
1.......2.3.....9....7.5.....83..7.......6..4..54..8.....6.7....2.....1.9...4...3 # 95793 # col-02-08-055
.2.4..7.........2........94.9.3...7...825.3.......1.....5..86...4.9....71........ # 95750 # col-02-08-056
.6.4..7......6..24........9.9.3...7.8....53.......1.....5...6...4.9....71....8... # 95745 # col-02-08-057
.2.4..7......3..2........94.9.2...7......53....8..1.....5..8....4.9....71.....6.. # 95722 # col-02-08-058
.2.4..7.........2........94.9.2...7......53....8..1.....5.986...4.3....71........ # 95684 # col-02-08-059
.9.4..7.........29.....7..4.4.2...7.8...1........5....5.....3...6.9....7..1..86.. # 95683 # col-02-08-060
.2.4..7.........2........94.9.3...7...8..53....7..1.....5..86...4.9....7..1...... # 95656 # col-02-08-061
.2.4..7.........34........2.9.3...7.6....5.....8..1...5.....6...3.9....7..1..89.. # 95655 # col-02-08-062
.2.4..7.........34........2.9.2...7.6....5.....8..1...1.....6...3.9....7..5..89.. # 95647 # col-02-08-063
1.......2.3.....9.....75.....8.6.74......4.....5..98.....6.8....2.....1.9...4...3 # 95632 # col-02-08-064
1.......2.3.....9....7.5.....8.527...4...6.....5..98.....6.8....2.....1.9.......3 # 95631 # col-02-08-065
.2.4..7..........4.......32.9.2...7.6....5.....8..1.....1...6...3.9....75....89.. # 95630 # col-02-08-066
.2.4..7.........29.....9..4.9.3...7......53....8..1.....5..86...4.9....7..1...... # 95615 # col-02-08-067
.294..7.........29........4.9.3...7......53....8..1.....5..86...4.9....7..1...... # 95615 # col-02-08-068
13..7...2.......4....5.6.....6...8..7.......6..91..5.....8.7....4.....3.2...9...1 # 95614 # col-02-08-069
.2.4..7....6.....4.......9..9.3..27......53....8.1.6....5.......4.2....71....8... # 95609 # col-02-08-070

Best Suexrat9
.2.4.37.........32........4.4.2...7.8...5.........1...5.....9...3.9....7..1..86.. # 4543 # col-02-08-071
.2.4..7..6......29.....6..4.4.6...7.8....1.......5....5....83...6.9....7..1...... # 3828 # col-02-08-072
.2.4.37..........2.......34.4.2...7.8...5.........1...5.....9...3.9....7..1..86.. # 3736 # col-02-08-073
.2.4.37..........2.......34.4.2...7...8.5.........1...5.....9...3.9....7..1..86.. # 3463 # col-02-08-074
.2.4..7....6....2........94.9.3...7......53....8.1......5...6...6.9....7..1..8... # 3349 # col-02-08-075
.6.4..7.........24....2.....9.3...7......53..8....1.....5...6...4.9....71....89.. # 3305 # col-02-08-076
.2.4..7......8..2.3.......4.9.3...7......53.......19....5...6...4.9....7..1..8... # 3212 # col-02-08-077
.2.4..7.........2......6.94.9.3...7...1..5.....8...3........6...3.9....71.5..8... # 3082 # col-02-08-078
.2.4.37..........2.......34.4.2...7.8............51...5.....9...3.9....7..1..86.. # 3046 # col-02-08-079
.2.4..7..........2.......94.9.3...7......53....8..1.....5...6...462....71....8... # 3042 # col-02-08-080
.3.4..7.........328......4..9.3...7.....5.6.......19.35....8....2.9....7..1...... # 3041 # col-02-08-081
.2.4..7..................24.9.2...7.....5.3....8..19.25....8....6.9....7..1...6.. # 3029 # col-02-08-082
.3.4..7.........23.......94.923...7......5.....8.1......5...6...4.9....71....8... # 3009 # col-02-08-083

Best Suexratt
.2.4..7..........4..7....92.9.3...7......53....8.1......5...6...4.2....71....8... # 1770 # col-02-08-084
.2.4..7..........2.......94.9.3...7......53....8..1.....5...6...462....71....8... # 1655 # col-02-08-080
.2.4..7....6....2........94.9.3...7......53....8.1......5...6...6.9....7..1..8... # 1573 # col-02-08-075
.2.4..7.........2........94.9.2...7.8...5.........13..5....8...36.9....71.....6.. # 1567 # col-02-08-085
.2.4..7....6....24.......9..9.3...7......53....8.1.6....5.......4.2....71....8... # 1409 # col-02-08-086
.2.4..7..........4..6....92.9.3...7......53....8.1......5...6...4.2....71....8... # 1390 # col-02-08-087
coloin

Posts: 1733
Joined: 05 May 2005

I've updated the mini-list with coloin's puzzle:
Code: Select all
`.2.4.37.........32........4.4.2...7.8...5.........1...5.....9...3.9....7..1..86..  col-02-08-071`
it has the following output using the "10000 2" option with suexratt - 4483,719 which makes it the highest rating according to suexrat9

tarek

tarek

Posts: 2698
Joined: 05 January 2006

I am back from three days off.
I has a look on the last list of coloin and I checked the sublist "Best Suexrat9"
Several of these puzzles have highly surprising results. High "structural rating" (counting solutions above 150 milliseconds), easy to solve.
I red that using computer processing time as a rating ratio is somehow the most stupid thing one can imagine.
I have a worst case. I use also the print size as indicator.

Code: Select all
`020403700000000032000000004040200070800050000000001000500000900030900007001008600 # 4543 # col-02-08-071 `

has the following set:

Counting 250 milliseconds
Processing time 4s781
Print size 26 K.

Which are indicator for a puzzle that could be one of the most difficult, but in fact a puzzle that could be solved without computer help.

Note: Golden Nugget last version
Counting 175 milliseconds
Processing time 98 seconds
Print size 650 K

I'll prepare the solution for a post if anybody is interested, but I am not sure this thread is the right place to post it.
champagne
2017 Supporter

Posts: 6542
Joined: 02 August 2007
Location: France Brittany

I think denis is a bit harsh, the suexrat9 and perhaps more so the suexratt is a fairly good indicator of difficulty...and the node count is an indicator of the processing time, but as you say this puzzle, along with many others isnt up there. The "counting" that your program does perhaps mirrors the suexrat9. [What exactly is it counting...it cant be solutions [=1]]

I thought you were commenting on denis' "font", but now I realize you were serious..what is the print size ?

Anone care to comment on why this puzzle has such a high suexrat9..[low suexratt].

Does it have a weak spot......in which case where ?

C
coloin

Posts: 1733
Joined: 05 May 2005

Hi coloin,

1) Counting.

Before looking for cracking a puzzle, I check if it's a valid one. To do so, I count the number of solutions.
If the puzzle is valid the result is always 1.
This is significantly different from looking for a solution in T&E mode.
As noticed gsf, T&E can give a biased idea of the difficult. Counting not because you have to test all possible starts.

I think counting is a fast and good indicator of structural difficulty.
Gsf tries to built a compréhensive analysis of why it appears to be structuraly difficult, which is a plus.

BTW, the processing time I got for counting is in line whith a High "structural rating".

2) Print size

This is a little more than a joke, but not that much. The print size is the size of the print file produced by my solver.
It explains the path followed by the solver. From that file to the post I produce, there is a ratio somewhere in between 1 to 5 and 1 to 10.
The reason is very simple, the solver is in a developping state. I need information in excess to understand how it works.
Normally there is a good correlation between the processing time and the print file size. I have in mind at least one discrepancy reflecting specific weaknesses of the corresponding puzzle.

3) weak spot

This is a difficult subject. Regarding that puzzle, the start uses column 7 structure. ALS (r23c7) AHS/AC (r4568c7)
As far as I remind, this is very specific to that puzzle.

Code: Select all
`169    2      5p689   |4     1689    3      |7       15689   156V89ç 14a679 156789 4A56789 |15678 16789   5679   |158     3       2       13c679 156789 3C56789 |15678 12b6789 2B5679 |158     156W89è 4       --------------------------------------------------------------------1f369  4      35q69   |2     368À9   6É9é   |1358    7       15689   8      1F679  2k3679  |367   5       4g679  |1234    12469   169     2l3679 5R679  235679  |3678ã 34G6789 1      |23458   245689  5689    --------------------------------------------------------------------5      678â   24678   |1J367 123467  2467   |9       1248    13e8    246    3      2468á   |9     1I246   245h6  |12M4O58 12458   7       2479d  7d9D   1       |35H7Ì 23ê47   8      |6       245ë    3E5e    `

Code: Select all
`#[]f - 8r3c8   []1r1c1 - 1r4c1.f []6r1c1 - 6r1c89 = 6r3c8 - 8r3c8 []9r1c1 - 9r1c89 = 9r3c8 - 8r3c8#[]8r3c8 - 1r4c9   []5r4c3 - 5r1c3 = 5r1c89 - 5r23c7 = AC:r4568c7(5r468c7 - 8r468c7) = 8r23c7 - 8r3c8            []5r4c9 - 1r4c9 []5r4c7 - 5r23c7 .....#[]8r3c8 - 8r3c8   ]1r4c1.f - 8r3c8|# []1r4c9 - 8r3c8|# []1r4c7 - 1r23c7 = AC:r4568c7(1r458c7 - 8r468c7) = 8r23c7 - 8r3c8`

clear ch=1r458c7.í clear ch=1r1c89r3c8.í
Code: Select all
`#[]À - í   []8r1c9 - 8r23c7 = AC:r4568c7(8r468c7 - 1r458c7.í) []8r1c8 - 8r23c7 = AC:r4568c7(8r468c7 - 1r458c7)    []8r1c5 - 8r4c5.À []8r1c3 - 5r1c3 = 5r1c89.P - 5r23c7 = AC:r4568c7(5r468c7 - 1r458c7)#[]í - 8r4c9   []5r4c3.q - 5r1c3 = 5r1c89.P - 5r23c7 = AC:r4568c7(5r468c7.î - 1r458c7.í)    []5r4c9 - 8r4c9 []5r4c7 - 5r23c7 = AC:r4568c7(5r468c7.î - 1r458c7.í)#[]í - í   [] 8r4c5.À - í|# []8r4c9 - í|# []8r4c7 - 8r23c7 = AC:r4568c7(8r468c7.ï - 1r458c7.í)`
champagne
2017 Supporter

Posts: 6542
Joined: 02 August 2007
Location: France Brittany

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