Rating rules / Puzzles. Ordering the rules

Advanced methods and approaches for solving Sudoku puzzles

Postby denis_berthier » Fri May 16, 2008 7:52 am

CORRELATION RESULTS FOR GSF'S COLLECTION

The collection referred to here is not the last extended file but the version that contained 4820 puzzles. I didn't take the last version because it contains many puzzles for which the SER and SER-times are not computed (I guess this is what the value 0 means)
gsf provides the Q1, SER and XR ratings and the Q1 computation times (he also provides the SER computation times, but their format is not useable without transformation: e.g. 1h4m6s).

--------------------------------------------------------------------------------

SER vs Q1 : 0.41
SER vs sqr(Q1) : 0.53
SER vs sqr4(Q1) : 0.62
SER vs sqr6(Q1) : 0.65
SER vs sqr8(Q1) : 0.67
SER vs sqr16(Q1) : 0.69
SER vs log(Q1) : 0.72

This shows that SER is not correlated to Q1 but to log(Q1)
This is indeed the impression I had but this is now confirmed by statistics.

--------------------------------------------------------------------------------

XR vs Q1 : 0.66
XR vs sqr(Q1) : 0.73
XR vs sqr4(Q1) : 0.77
XR vs sqr6(Q1) : 0.77
XR vs sqr8(Q1) : 0.77
XR vs sqr16(Q1) : 0.77
XR vs log(Q1) : 0.77

This shows that XR is less correlated to Q1 than to sqr4(Q1),..., sqr16(Q1) or log(Q1)

--------------------------------------------------------------------------------

ER vs XR : 0.64
ER vs sqr(XR) : 0.73
ER vs sqr4(XR) : 0.78
ER vs sqr6(XR) : 0.80
ER vs sqr8(XR) : 0.81
ER vs sqr16(XR) : 0.82
ER vs log(XR) : 0.83

This shows that ER is less correlated to XR than to sqr4(XR),..., sqr16(XR) or log(XR)

--------------------------------------------------------------------------------
Comments:

We can ask: how is it possible that SER is correlated to log(Q1), XR is correlated to log(Q1) and SER is more correlated to log(XR) than to XR?
Don't forget that we are in a high dimensional space (here R^4820) and there are many ways several unit vectors can be close to each other.

The Q1 scaling is best considered as exponential wrt to the other usual scalings.

--------------------------------------------------------------------------------

Finallly, what can be said of the computation times?

Q1-times vs Q1 : 0.38
Q1-times vs log(Q1) : 0.23
As Q1-times may be 0, one can't compute Q1 vs log(Q1-times), but
Q1 vs sqr16(Q1-times) : 0.50

There doesn't seem to be any correlation between Q1 and Q1-times. But this may be due to the imprecision in Q1-times (the unit is the second and many values are 0).
denis_berthier
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Postby coloin » Fri May 16, 2008 3:50 pm

Indeed.

I think the gsf Taxonomy has a few errors, notably the -q1 rating for Golden Nuggett.

Tariq and I have been using the sx9/sxt rating based on dukuso's suexrat9 and suexratt programs. [Not the gsf xrate] The program does a node count of 1000 morphs of the puzzle - the sxt is the node count of the worst 2%. Thus the sxt is a sort of "global" hardness rating - The gsf -q1 rating is specific to an extent too.

As ever no rating system we have got has approached reasonable correalation. And SE just takes too long - particularly in a few puzzles. Notably the puzzles Obi-Whan has found hard.

In particular I am tabulating a new collection of "hardest"......which may just blow a few lids.

There is a problem with hard puzzles which have an initial single insertion.

I have a puzzle with 5 singles and then has the sxratt/sx9 better than Golden Nuggett. Its gsf rating is high despite the 5 singles - normally this reduces the sx9 and -q1 ratings. The SE is 10.9 [21 plus 5 inserted singles clues]. The sx9 seems to give false highs when there are singles initially. Not so here. Suggestions for name please.

Over the weekend I will finalize the list.

C
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Posts: 1637
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Postby denis_berthier » Fri May 16, 2008 4:47 pm

coloin wrote:I think the gsf Taxonomy has a few errors, notably the -q1 rating for Golden Nuggett.

I don't think one can define a rating independent of any specific hypotheses. I defined the NRCZT-rating of P based on only the maximum length of the nrczt-chains necessary to solve P. SER is based on another particular list of rules. SUEX9, SUEXT and Q1 are based on still other assumptions.
As a result of these different approaches, for some puzzles, there are large discrepancies between the different ratings.
It is nevertheless noticeable that, statistically, most of these ratings have reasonably strong correlations.
As for the Q1-rating, its discrepancies can only seem larger, as it corresponds statistically to the choice of an exponential scale wrt to the other ratings.

coloin wrote:I am tabulating a new collection of "hardest"......which may just blow a few lids.
Over the weekend I will finalize the list.

Will you provide some of the above ratings for the puzzles in it?
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Postby coloin » Fri May 16, 2008 5:41 pm

denis_berthier wrote:Will you provide some of the above ratings for the puzzles in it?

I generally do

Gsfs -q1 appears to have a scientific principle
Suexratt has been modified from suexrat9.
Suexrat9 gives the average node count
suexratt gives the bottom 2% of all the tries.

Here is two puzzles with previous bests for comparison.

I have morphed the puzzles to be similar to Golden Nuggett [itself morphed from original]
Code: Select all
             
1.......7.2.4...6...3...5...9..86........4.8....2..9....5.1.....6.8...2.7.......3     Golden Nuggett     
1.......7.2.4...6...3...5...9.68........94.8.2............5.1...6.9...2.7.......3     tarek-1801         
1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1...     Silver Plate     
1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3...     Bronze Medalian   
1.......7.2.4...6...3...5...8.6.........3.......2.9.4...5...3...9...8.2.7.......1     m_b_metcalf       

Golden Nuggett    - probabaly the top rated puzzle  [so far !]
tarek-1801        - No 2 on gsfs -q1, long processing time ?
Silver Plate      - Nuggett pattern - better sxt
Bronze Medalian   - Nuggett pattern - with a single
m_b_metcalf       - 20 clues

Code: Select all
Output from gsfs -q1 and dukuso suexratt                                                                           
                                                                                                                   
C:\temp>sudoku -q1 test9.txt                                                                                       
1.......7.2.4...6...3...5...9..86........4.8....2..9....5.1.....6.8...2.7.......3 # 96582 FNP C21.m/M2.1.164025   
1.......7.2.4...6...3...5...9.68........94.8.2............5.1...6.9...2.7.......3 # 99077 FNBP C21.m/M3.1282.414   
1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1... # 95667 FNP C21.m/M2.1.314928   
1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3... # 95072 FNP C21.m/M2.8.5740     
1.......7.2.4...6...3...5...8.6.........3.......2.9.4...5...3...9...8.2.7.......1 # 95103 FNP C20.m/S2.a/M2.3.63423
                                                                                                                   
C:\temp>suexratt test9.txt 10000 2                                                                                 
rating:   3383 ,    2019 , 1.......7.2.4...6...3...5...9..86........4.8....2..9....5.1.....6.8...2.7.......3       
rating:   2387 ,    1483 , 1.......7.2.4...6...3...5...9.68........94.8.2............5.1...6.9...2.7.......3       
rating:   3302 ,    2169 , 1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1...       
rating:   3296 ,    2011 , 1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3...       
rating:   1287 ,     786 , 1.......7.2.4...6...3...5...8.6.........3.......2.9.4...5...3...9...8.2.7.......1

Code: Select all
+---+---+---+                         
|1..|...|..7|                         
|.2.|4..|.6.|                         
|..3|...|5..|                         
+---+---+---+                         
|.9.|.86|...|                         
|...|..4|.8.|                         
|...|2..|9..|                         
+---+---+---+                         
|..5|.1.|...|                         
|.6.|8..|.2.|                         
|7..|...|..3|                         
+---+---+---+  Golden Nuggett         
                                     
+---+---+---+                         
|1..|...|..7|                         
|.2.|4..|.6.|                         
|..3|...|5..|                         
+---+---+---+                         
|.9.|68.|...|                         
|...|.94|.8.|                         
|2..|...|...|                         
+---+---+---+                         
|...|.5.|1..|                         
|.6.|9..|.2.|                         
|7..|...|..3|                         
+---+---+---+  tariq-1801             
                                     
                                     
+---+---+---+                         
|1..|...|..7|                         
|.2.|4..|.6.|                         
|..3|...|5..|                         
+---+---+---+                         
|.9.|.4.|...|                         
|...|.62|.4.|                         
|...|9..|8..|                         
+---+---+---+                         
|..5|...|..3|                         
|.6.|2..|.8.|                         
|7..|..1|...|                         
+---+---+---+ Silver Plate           
                                     
                                     
+---+---+---+                         
|1..|...|..7|                         
|.2.|4..|.6.|                         
|..3|...|5..|                         
+---+---+---+                         
|.9.|.82|...|                         
|...|.9.|.8.|                         
|...|6..|4..|                         
+---+---+---+                         
|..5|...|1..|                         
|.6.|8..|.2.|                         
|7..|..3|...|                         
+---+---+---+ Bronze Medalian         
                                     
                                     
                                     
+---+---+---+                         
|1..|...|..7|                         
|.2.|4..|.6.|                         
|..3|...|5..|                         
+---+---+---+                         
|.8.|6..|...|                         
|...|.3.|...|                         
|...|2.9|.4.|                         
+---+---+---+                         
|..5|...|3..|                         
|.9.|..8|.2.|                         
|7..|...|..1|                         
+---+---+---+  m_b_m                 


I havnt done SE 121 !

C
coloin
 
Posts: 1637
Joined: 05 May 2005

Postby coloin » Fri May 16, 2008 6:00 pm

Reading your posts heres a selection from the archive - unlabelled

Code: Select all
rating:   1132 ,     728 , .......39........5..3.6.8....8.3...6.7...2...1..4.......9.8..5..2...16..4..7.....       
rating:   2065 ,    1251 , .....1.39........5..3.5..8...8.9...67....2...1..4.......9.8..5..2....6..4..7.....       
rating:   2350 ,    1004 , ..1..4.......6.8.5...9.....8.....7.........235...7.6.83...8...6..92......4...1...       
rating:   1884 ,    1036 , .......39.......65..3.6.8....8.9...6.7...2...1..4.......9.8..5......1...42.7.....       
rating:   2295 ,    1438 , .......9......1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2.7..6..4.....3..       
rating:   2001 ,    1025 , ........9.....1.35..3.5..8...8.....6.7...2...1..4.......9.8..5..2.1..6..4....7...       
rating:   2114 ,     695 , ..1..4.......6.3.5...9.....5.....7.8.......238...7.6..3...8...6..92......4...1...       
rating:   1564 ,     590 , .....4.......6.3.7.1.9.....8.....7.3.......255...7.6..3...8...6..92......4...1...       
rating:   2661 ,     952 , ...1...3.1.......5..3.5.8....8.9...6.7...2......4..9....9.8..5..2....6..4..7.....       
rating:   1665 ,     745 , ..1..4.......6.3.5...9.....5.....7.........288...7.6..3...8...6..92......4...1.3.       
rating:   2000 ,     638 , ..1..4.......6.3.5...9.....5.....7.8.......2.8...7.65.3...8...6..92......4...1...       
rating:   1866 ,    1182 , .......38.....1..5..3.5..9...8.9...6.7...2...1..4.......9.6..8..2....6..4..7.....       
rating:   1793 ,    1064 , ..1..4.......6.3.5...9..7..8...7...3.......2.5.3...6..3...8...6..92......4...1...       
rating:   1473 ,     791 , .1...4.......3.8.5...9.....8.....7.3.......2.5...7.6..3...8...6..92......4...1.3.       
rating:   1441 ,     913 , .2.....38........5..3.5..9...8.9...6.7...2...1..4.......9.8..5......16..4..7.....       
rating:   1488 ,    1012 , .7.....39........5..3.6.8....8.3...6.....2...1..4.......9.8..5..2...16..4..7.....       
rating:   1567 ,     716 , ..1..4.......6.3.5...9.....5.....7.8.......2.8...7.6..3...8...6..92......4...1.3.       
rating:   2304 ,    1336 , .......38.....1..5..3.5.9....8.9...6.7...2...1..4.......9.8..5.2.....6..4..7.....       
rating:   1432 ,     896 , ...1...3.........5..3.6.8....8.9...6.7...2......4.......9.8..5..2...16..4..7..9..       
rating:   1904 ,     862 , ..1..4.......6.3.5...9.....8.....7.........2.5...7..683...8...6.892......4...1...       
rating:   1351 ,     831 , .......39........5..3.6.8....8.9...6.7...2...1..4.......9.5..8..2...16..4..7.....       
rating:   1283 ,     872 , .......38...2....5..3.5..9...8.9...6.7...2...1..4.......9.8..5......16..4..7.....       
rating:   1179 ,     710 , 1......39.......85..3.5......8.9...6.7...2......4.......9.8..5..2.1..6..4..7.....       
rating:   1288 ,     765 , .....1.39........5..3.6..8...8.9...6.7...2....1.4.......9.8..5..2....6..4..7.....       
rating:   2052 ,     605 , ..1..4.......6.5.8...9.....8.....7.3.......255...7.6..3...8...6.9.2......4...1...       
rating:   1627 ,     798 , ..1..4.......6.3.5...9.....8.....7.........2.5...7.6.83...8...6..9..1.8..4.2.....       
rating:   1198 ,     821 , 4......39........5..3.6..8...8.9...6.7...2...1..4.......9.8..5..2...16.....7.....       
rating:   1230 ,     663 , .......39........5..6.3.8....8.9...6.7...2...1..4.......9.8..5..2...16..4..7.....       
rating:   1707 ,    1047 , .......39.....1.....3.5.8....8.9...67....21.....4..5....6.8..5..2....6..4..7.....       
rating:   1411 ,     725 , ..1..48......6.3.5...9.....8.....7....6....285...7....3...8...6..9..2....4.1.....       
rating:   1860 ,     688 , .2.4..7.........32........4.9.2...7...6.5....8....1...5....89...3.9....7..1...6..       
rating:   1146 ,     662 , .......35.4.........3.5.8....8.9...6.7...2...1.....9....9.8..5..2...16..4..7.....       
rating:   1909 ,    1002 , .51..4.......6.8.5...9.....8.....7.3.......2.3...7.6..5...8...6..92......4...1...       
rating:   1230 ,     610 , ..1..4.......6.3.5...9.....8.....7.........2.5.6.7.4.83...8...6..92......4...1...       
rating:   1503 ,     969 , 1......39...........3.5.8....8.9...6.7...25.....4.......9.8..5..2.1..6..4..7.....       
rating:   1200 ,     807 , .7......9.......65..3.5.8....8.9...6.....23..1..4.......9.8..5..2.1.....4..7.....       
rating:   1663 ,     672 , ..1..4.......6.5.7...9.....8.....7.3.......255...7.6..3...8...6..92......4...1...       
rating:   1889 ,     737 , .......39.......65..3.6.8....8.9...6.7.......1..4..2....9.8..5..2...1...4..7.....       
                                                                                                                   
                                                                                                                   
                                                                                                                   
                                                                                                                   
.......39........5..3.6.8....8.3...6.7...2...1..4.......9.8..5..2...16..4..7..... # 97631 FNP C21.m/M3.886.599     
.....1.39........5..3.5..8...8.9...67....2...1..4.......9.8..5..2....6..4..7..... # 97512 FNP C21.m/M2.1.570807     
..1..4.......6.8.5...9.....8.....7.........235...7.6.83...8...6..92......4...1... # 97503 FNP C21.m/M3.820.648     
.......39.......65..3.6.8....8.9...6.7...2...1..4.......9.8..5......1...42.7..... # 97099 FNP C21.m/M2.1.164025     
.......9......1..5..3.5.8....8.9...6.7...2...1..4.......9.8..5..2.7..6..4.....3.. # 96821 FNP C21.m/M3.1407.377     
........9.....1.35..3.5..8...8.....6.7...2...1..4.......9.8..5..2.1..6..4....7... # 96798 FNP C21.m/M2.1.157464     
..1..4.......6.3.5...9.....5.....7.8.......238...7.6..3...8...6..92......4...1... # 96724 FNP C21.m/M3.825.644     
.....4.......6.3.7.1.9.....8.....7.3.......255...7.6..3...8...6..92......4...1... # 96403 FNP C21.m/M2.4.19680     
...1...3.1.......5..3.5.8....8.9...6.7...2......4..9....9.8..5..2....6..4..7..... # 96401 FNP C21.m/M2.1.223074     
..1..4.......6.3.5...9.....5.....7.........288...7.6..3...8...6..92......4...1.3. # 96383 FNP C21.m/M2.2.157440     
..1..4.......6.3.5...9.....5.....7.8.......2.8...7.65.3...8...6..92......4...1... # 96330 FNP C21.m/M2.1.328050     
.......38.....1..5..3.5..9...8.9...6.7...2...1..4.......9.6..8..2....6..4..7..... # 96317 FNP C21.m/M2.1.190269     
..1..4.......6.3.5...9..7..8...7...3.......2.5.3...6..3...8...6..92......4...1... # 96230 FNP C21.m/M2.6.9837       
.1...4.......3.8.5...9.....8.....7.3.......2.5...7.6..3...8...6..92......4...1.3. # 96050 FNP C21.m/M2.39.168       
.2.....38........5..3.5..9...8.9...6.7...2...1..4.......9.8..5......16..4..7..... # 96005 FNP C21.m/M2.1.347733     
.7.....39........5..3.6.8....8.3...6.....2...1..4.......9.8..5..2...16..4..7..... # 95977 FNP C21.m/M2.3.32805     
..1..4.......6.3.5...9.....5.....7.8.......2.8...7.6..3...8...6..92......4...1.3. # 95974 FNP C21.m/M3.1598.332     
.......38.....1..5..3.5.9....8.9...6.7...2...1..4.......9.8..5.2.....6..4..7..... # 95909 FNP C21.m/M2.1.157464     
...1...3.........5..3.6.8....8.9...6.7...2......4.......9.8..5..2...16..4..7..9.. # 95880 FNP C21.m/M2.9.17496     
..1..4.......6.3.5...9.....8.....7.........2.5...7..683...8...6.892......4...1... # 95819 FNP C21.m/M2.9.5832       
.......39........5..3.6.8....8.9...6.7...2...1..4.......9.5..8..2...16..4..7..... # 95811 FNP C21.m/M2.2.154160     
.......38...2....5..3.5..9...8.9...6.7...2...1..4.......9.8..5......16..4..7..... # 95802 FNP C21.m/M2.11.3576     
1......39.......85..3.5......8.9...6.7...2......4.......9.8..5..2.1..6..4..7..... # 95800 FNP C21.m/M2.15.3496     
.....1.39........5..3.6..8...8.9...6.7...2....1.4.......9.8..5..2....6..4..7..... # 95770 FNP C21.m/M2.19.690       
..1..4.......6.5.8...9.....8.....7.3.......255...7.6..3...8...6.9.2......4...1... # 95718 FNP C21.m/M2.7.7496       
..1..4.......6.3.5...9.....8.....7.........2.5...7.6.83...8...6..9..1.8..4.2..... # 95628 FNP C21.m/M2.5.34112     
4......39........5..3.6..8...8.9...6.7...2...1..4.......9.8..5..2...16.....7..... # 95592 FNP C21.m/M2.31.211       
.......39........5..6.3.8....8.9...6.7...2...1..4.......9.8..5..2...16..4..7..... # 95591 FNP C21.m/M3.1878.282     
.......39.....1.....3.5.8....8.9...67....21.....4..5....6.8..5..2....6..4..7..... # 95585 FNP C21.m/M2.5.32800     
..1..48......6.3.5...9.....8.....7....6....285...7....3...8...6..9..2....4.1..... # 95584 FNP C21.m/M2.1.321489     
.2.4..7.........32........4.9.2...7...6.5....8....1...5....89...3.9....7..1...6.. # 95574 FNP C21.m/M2.1.209952     
.......35.4.........3.5.8....8.9...6.7...2...1.....9....9.8..5..2...16..4..7..... # 95571 FNP C21.m/M2.10.3280     
.51..4.......6.8.5...9.....8.....7.3.......2.3...7.6..5...8...6..92......4...1... # 95564 FNP C21.m/M2.8.4920       
..1..4.......6.3.5...9.....8.....7.........2.5.6.7.4.83...8...6..92......4...1... # 95551 FNP C21.m/M2.37.177       
1......39...........3.5.8....8.9...6.7...25.....4.......9.8..5..2.1..6..4..7..... # 95531 FNP C21.m/M2.17.1155     
.7......9.......65..3.5.8....8.9...6.....23..1..4.......9.8..5..2.1.....4..7..... # 95507 FNP C21.m/M2.8.4920       
..1..4.......6.5.7...9.....8.....7.3.......255...7.6..3...8...6..92......4...1... # 95507 FNP C21.m/M2.1.164025     
.......39.......65..3.6.8....8.9...6.7.......1..4..2....9.8..5..2...1...4..7..... # 95506 FNP C21.m/M2.1.144342   


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Postby champagne » Fri May 16, 2008 6:44 pm

Hi coloin,
I checked your list here above.
I got the following processing time (seconds)
Code: Select all
100000007020400060003000500090086000000004080000200900005010000060800020700000003     Golden Nuggett 78
100000007020400060003000500090680000000094080200000000000050100060900020700000003     tarek-1801   45
100000007020400060003000500090040000000062040000900800005000003060200080700001000     Silver Plate  127
100000007020400060003000500090082000000090080000600400005000100060800020700003000     Bronze Medalian  46
100000007020400060003000500080600000000030000000209040005000300090008020700000001     m_b_metcalf  15


No surprise for Golden Nugget and m-b-metcaf although I have them under different starting patterns.

Silver plate is a puzzle I likely never tested.
Has it been published in the hardest thread with another arrangement.

Anyway, I have a processing time significantly higher than for Golden Nugget, so I have to investigate.
I start checking of the second list and I am waiting now for your new set of puzzles.
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Postby gsf » Fri May 16, 2008 6:53 pm

coloin wrote:
denis_berthier wrote:Will you provide some of the above ratings for the puzzles in it?

I generally do

Gsfs -q1 appears to have a scientific principle

-q2 is a refinement that seems closer to our intuition on hardness
its a bit faster than -q1
it esitmates the amount of work done by a candidate degree ordered backtrack solver that propagates { singles locked-candidates }
here are the -q2 ratings for the 5 hardest you just posted
Code: Select all
1.......7.2.4...6...3...5...9..86........4.8....2..9....5.1.....6.8...2.7.......3 # 99222 FNBP C21.m
1.......7.2.4...6...3...5...9.68........94.8.2............5.1...6.9...2.7.......3 # 98988 FNBP C21.m
1.......7.2.4...6...3...5...9..4........62.4....9..8....5.....3.6.2...8.7....1... # 98036 FNBP C21.m
1.......7.2.4...6...3...5...9..82.......9..8....6..4....5...1...6.8...2.7....3... # 98041 FNBP C21.m
1.......7.2.4...6...3...5...8.6.........3.......2.9.4...5...3...9...8.2.7.......1 # 97869 FNBP C20.m/S2.a
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Postby champagne » Fri May 16, 2008 7:05 pm

Hi coloin,

My own list of hardest inyour second set.
1) No surprise, it is not the same ranking as Gsf, but this is not new
2) Some of theses puzzles enter my short list of hardest

Code: Select all
000000090000001005003050800008090006070002000100400000009080050020700600400000300 # 96821 FNP C210m/M3014070377   26s765
000000009000001035003050080008000006070002000100400000009080050020100600400007000 # 96798 FNP C210m/M2010157464   34s641
000100030100000005003050800008090006070002000000400900009080050020000600400700000 # 96401 FNP C210m/M2010223074   43s031
000000038000001005003050090008090006070002000100400000009060080020000600400700000 # 96317 FNP C210m/M2010190269   29s156
070000039000000005003060800008030006000002000100400000009080050020001600400700000 # 95977 FNP C210m/M203032805    28s469
000000038000001005003050900008090006070002000100400000009080050200000600400700000 # 95909 FNP C210m/M2010157464   32s766
000100030000000005003060800008090006070002000000400000009080050020001600400700900 # 95880 FNP C210m/M209017496    39s594
100000039000000000003050800008090006070002500000400000009080050020100600400700000 # 95531 FNP C210m/M201701155    29s109
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Postby coloin » Fri May 16, 2008 8:39 pm

Thanks for that, the -q2 option will be useful !

champagne wrote:Silver plate is a puzzle I likely never tested. Has it been published in the hardest thread with another arrangement ?
No,....I initially posted two new puzzles [SP and BM] for denis, note I morphed the other puzzles - which makes it easier to see whats going on in the generating processes. Note the manipulated similarities in the puzzles in boxes12347 . I wonder if there is value in doing this for all puzzles......it certainly makes GN look more pleasant. Can this be utilized for selective puzzle making ?

The list was for denis to perform a correalation , there may be old and new puzzles in this list. The suexratt setting for these puzzles was 1000 2.
Thinking about it for a bit........I dont think this unlabelled batch is a good representation for correalation purposes.....more thought needed on that.

A quick run with -q2 gave this puzzle, not quite up to Easter Monster.

Code: Select all
+---+---+---+
|...|...|..7|
|.2.|4..|.6.|
|1..|...|5..|
+---+---+---+
|.9.|..2|.4.|
|...|8..|6..|
|6..|9..|...|
+---+---+---+
|..5|..3|...|
|.3.|.8.|.2.|
|7..|..4|..1|
+---+---+---+ Tungston Rod

Code: Select all
q2         q1        sx9     sxt
# 99307    # 99383   # 2938  # 1533 ,
........7.2.4...6.1.....5...9...2.4....8..6..6..9.......5..3....3..8..2.7....4..1 # 99307 FNBP C21.m/M3.310.1714


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Postby champagne » Sat May 17, 2008 6:26 am

coloin wrote:No,....I initially posted two new puzzles [SP and BM] for denis, note I morphed the other puzzles - which makes it easier to see whats going on in the generating processes.


I had a look to the print, it appears that SP has been really tougher to solve for it than GN. SP is now my hardest

I have another question on "morphing" and "canonical form". Where is described the rule applied to do it in the form used in that forum?

Altenatively, is there a tool I can use to check my files and keep them in the same form.


coloin wrote:Note the manipulated similarities in the puzzles in boxes12347 . I wonder if there is value in doing this for all puzzles......it certainly makes GN look more pleasant. Can this be utilized for selective puzzle making ?


The solver does not care, but I agree with you. The SK loop for example is much easier to detect and to process if it appears always in the same cells;

coloin wrote:A quick run with -q2 gave this puzzle, not quite up to Easter Monster.

Code: Select all
q2         q1        sx9     sxt
# 99307    # 99383   # 2938  # 1533 ,
........7.2.4...6.1.....5...9...2.4....8..6..6..9.......5..3....3..8..2.7....4..1 #



Nothing special on my side for that puzzle
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Postby denis_berthier » Sat May 17, 2008 7:27 am

Coloin, you're right: correlation results are meaningful only for large samples. I'll therefore wait for your whole sample.

Moreover, such results are valid only for the range of values sufficiently represented in the sample.

gsf's collection is interesting because it is large and it has many puzzles on the whole range of ratings. On the other hand, as it has been manually assembled, it can't be guaranteed to be unbiased. The question is: are human puzzle creators somehow biased in the way they build their puzzles?

It'd be interesting to have your collection in the same format as gsf's, so that we can glue them easily and have a broad range of values for the ratings.


gsf, it'd be interesting to have the new q2 rating for your whole collection (or the command line to compute it for a file in the gsf format). It seems that q1 and q2 should be strongly correlated.

For q2, what do you mean by "locked-candidates".
Do they include all the Naked Pairs, Triplets and Quads (or only the Pairs, as suggested by the 2 in q2)?
Do they include their Hidden counterparts (for symmetry reasons)?
Do they include their Super-Hidden counterparts, i.e. fish (for super-symmetry reasons)?

If such is the case, I think you should consider adding elementary row/column interactions with blocks, as they are logically much simpler than Triplets or Quads. They come indeed immediately after the Singles.
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Postby tarek » Sat May 17, 2008 12:02 pm

denis_berthier wrote:On the other hand, as it has been manually assembled, it can't be guaranteed to be unbiased.
I would say that it is Extremely biased. My contributions on one hand were subject to an EXTREME selection bias. I'm not sure how it can be normalised.

denis_berthier wrote:I think you should consider adding elementary row/column interactions with blocks, as they are logically much simpler than Triplets or Quads. They come indeed immediately after the Singles
which is also referred to as "locked candidates":D

coloin wrote:I am tabulating a new collection of "hardest"......which may just blow a few lids
What happend to: "I'm glad that we are no longer searching for hardest puzzles":?::D

Looking forward to see it though:D

tarek


P.S. SP is the 2nd puzzle to have a backdoor size 2 under gsf's FNBTHXYKO set of techniques (bring them on:D )
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Postby denis_berthier » Sat May 17, 2008 12:24 pm

tarek wrote:
denis_berthier wrote:On the other hand, as it has been manually assembled, it can't be guaranteed to be unbiased.
I would say that it is Extremely biased. My contributions on one hand were subject to an EXTREME selection bias. I'm not sure how it can be normalised.

It is obviously biased if we consider the global distribution of puzzles wrt to the complexities. But I was thinking of other types of bias within each complexity class.

Can you say more about your bias?
Was it based only on high rating or did you have any other criterion?

One of the criteria I would choose if I was a puzzle creator is long chains (more fun) but relatively few partial chains (otherwise it is impossible to find the useful ones) - whatever type of chains one chooses to consider: nrczt, ALS,... What do you think of this?
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Postby tarek » Sat May 17, 2008 2:29 pm

denis_berthier wrote:Can you say more about your bias?
Was it based only on high rating or did you have any other criterion?

Most of my contributions within the q1 taxonomy list can be described as:
*. Closely related to the diagonal pattern seed described by coloin (minimised from 16 clue template+Full central box)
*. q1>95000 or (FN)-backdoor size >2
*. Sx9>900
*. difficult 1st move (a guess if FNBTHXYKO is the set of solving techniques)


denis_berthier wrote:One of the criteria I would choose if I was a puzzle creator is long chains (more fun) but relatively few partial chains (otherwise it is impossible to find the useful ones) - whatever type of chains one chooses to consider: nrczt, ALS,... What do you think of this?
This closely resembles:
1. A benchmark list (singles + one technique to solve)
2. One-trick pony puzzles (Ruud's terminology): which means that a technique set (x) will require ONLY ONE STEP outside the technique set (x) to solve.

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Postby denis_berthier » Sat May 17, 2008 5:31 pm

tarek wrote:
denis_berthier wrote:One of the criteria I would choose if I was a puzzle creator is long chains (more fun) but relatively few partial chains (otherwise it is impossible to find the useful ones) - whatever type of chains one chooses to consider: nrczt, ALS,... What do you think of this?
This closely resembles:
1. A benchmark list (singles + one technique to solve)
2. One-trick pony puzzles (Ruud's terminology): which means that a technique set (x) will require ONLY ONE STEP outside the technique set (x) to solve.

These are two extreme cases.
My computations show that:
- statistically, the number of partial nrczt-chains in a puzzle increases exponentially with its NRCZT-rating;
- within each NRCZT class, there is a large variation in the number of such partial chains.

This leaves the possibility of choosing puzzles that need long chains but have a limited number of parasitic partial chains.
Such puzzles could be obtained with a random generator, filtering out for a predefined NRCZT-rating and then filtering out for a relatively small number of chains within this class.

Although I'm speaking of my preferred nrczt-chains and I've'nt done any computations for chains based on subsets instead, I think all this applies equally to them.
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