## Puzzles Usage in a Presentation of a New Rating of Puzzles

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

### Re: Detail of the New Rating of Puzzl is Included

tknottet wrote:I illustrate the relation of the puzzles.

Pa(23-clue)>>>>>>>>(one clue elimination)>>>>>>>>Pb
V V
transposition and number permutation transposition and number permutation
V V
Pc>>>>>>>>>>>>>>>>(one clue eliminated)>>>>>>>>Pd(minimal version)
V
transposition and number permutation
V
(Pe) Pf

Did you propose to check Pf?
I misunderstood that you proposed to clarify which causes the difference of rating value, "clue elimination" or "transposition and number permutation". I already started the rating of Pc. It will take a few days. After that I will rate Pf.

I don't understand why "transposition and number permutation" appears a second time in the second column.
Anyway, in order to see the effect of these operations on R, it's interesting to compare R(Pa) with R(Pc) and also R(Pb) with R(Pd) and R(Pf)

Your current result is R(Pa) ≠ R(Pd), right ?
denis_berthier
2010 Supporter

Posts: 1269
Joined: 19 June 2007
Location: Paris

### Re: Detail of the New Rating of Puzzl is Included

denis_berthier wrote:
tknottet wrote:I illustrate the relation of the puzzles.

Pa(23-clue)>>>>>>>>(one clue elimination)>>>>>>>>Pb
V V
transposition and number permutation transposition and number permutation
V V
Pc>>>>>>>>>>>>>>>>(one clue eliminated)>>>>>>>>Pd(minimal version)
V
transposition and number permutation
V
(Pe) Pf

Did you propose to check Pf?
I misunderstood that you proposed to clarify which causes the difference of rating value, "clue elimination" or "transposition and number permutation". I already started the rating of Pc. It will take a few days. After that I will rate Pf.

I don't understand why "transposition and number permutation" appears a second time in the second column.
Anyway, in order to see the effect of these operations on R, it's interesting to compare R(Pa) with R(Pc) and also R(Pb) with R(Pd) and R(Pf)

Your current result is R(Pa) ≠ R(Pd), right ?

Yes R(Pa) ≠ R(Pd).
I intended to illustrate followings:
Pb > transposition and number permutation > Pd(minimal version)
Pd(minimal version) > transposition and number permutation > Pf
But consecutive space(blank) symbols are displayed as one symbol.
To see my illustration(picture), please use "quote".
(I use Firefox browser, but it may not be the matter.)

To shorten calculation time, my rating code works as follows,
In case
Pxy is created by y-assumption after x-assumption.
(from P1, P1(x) is created P1=P1(x) for recursion; from P1, P1(y) is created)
Pyx is created by x-assumption after y-assumption.
My rating assume that R(Pxy)=R(Pyx).
If R(Pxy) is already calculated, R(Pyx) is not calculated. R(Pxy) is used in place of R(yx).
Among isomorphs, the order of appearances varies.
As you wrote, non confluence problems may explain my Imam_bayildi problem.
Are (any of) rules employing chain are known to be non confluent?
My rules r10 to r13 are employ chains.
r10 uses only strong links between same number.
r11 uses strong links and weak links between same number.(of course odd links in order must be strong)
r12 uses only strong links but between same number and between different numbers.
As you know, if the both end of a chain are in a same unit, some candidate(s) eliminated.
In r11 and r13, one or two candidates may be eliminated, even if the both end are not in a same unit.
[UPDATE]
I was confused.
Of course, if T is not confluent, my rating differs among isomorphs.
This time I want to know is:
thinking 2 puzzles P and P-
where a candidate C1 is eliminated from T to make P-;
if T can eliminate a candidate C2(other than C1) from P,
can T eliminate a candidate C2 from P-?
The relation between P and P- resembles the relation of Pa and Pb,
because "clue elimination" is "adding candidates".
In the other hand, this problem maybe problem of rule order, which denis_berthie rwrote previously.
tknottet

Posts: 24
Joined: 15 February 2015

### Re: Detail of the New Rating of Puzzl is Included

tknottet wrote:
denis_berthier wrote:Your current result is R(Pa) ≠ R(Pd), right ?

Yes R(Pa) ≠ R(Pd).
I intended to illustrate followings:
Pb > transposition and number permutation > Pd(minimal version)
Pd(minimal version) > transposition and number permutation > Pf
But consecutive space(blank) symbols are displayed as one symbol.

I could see the consecutive spaces when I edited your post, but not in my browser (if you type consecutive spaces in html, it can "see" only one of them).
In html, you should use "&nbsp;" instead of spaces, but I don't know if the software of this forum accepts this.
If you type no-break spaces (alt-space) instead of mere spaces, I think it will work. (It works on my Mac.)

tknottet wrote:Among isomorphs, the order of appearances varies.
As you wrote, non confluence problems may explain my Imam_bayildi problem.
[...]
Of course, if T is not confluent, my rating differs among isomorphs.

I wouldn't be so affirmative. Even if there is some confluence problem, we can't be sure it is the cause of what you see in this particular example.

Without knowing your chain rules precisely, I can't say much. Many sets of chain rules have the confluence property: reversible chains (xy-chains, AICs,...) and non-reversible ones (braids, g-braids, ...). Other sets don't: whips, g-whips,... (but, as I said before, effective occurrences of problems are very rare). Also, you spoke of "vectors"; I never heard of such a technique.

One way you can have an idea whether your set of rules has a problem with confluence is checking them individually for a stronger (but easier to check) property (stability for confluence): do you have a rule that can be applied in some case to produce an elimination of some candidate x, and such that no rule in your set could still eliminate x if another candidate y had been eliminated (or asserted) before? Needless to check this with the basic rules (Singles+locked-candidates+Subsets) we mentioned before (we know that set has the confluence property).

The only alternative approach I can imagine is, try to spot precisely where the divergence in your example occurs and to see what happens at that point in each case: which rule is applied or not, why it is applied in one case and not in the other, ... anything like that.
denis_berthier
2010 Supporter

Posts: 1269
Joined: 19 June 2007
Location: Paris

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

Using the code tag is the best way I know of to show things where the spacing needs to be controlled. The UTF version of non-breaking space    (alt-space) does work, but with a variable width font it doesn't always work out well in practice (depending on what you are trying to do). It adds extra space just fine, but you won't be able to line things up except at the start of the line.

JasonLion
2017 Supporter

Posts: 641
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

Hello tknottet (and Denis),

I've coded your rating method, and tried it with some simpler versions of "T", on the puzzles that are currently listed on your web page.
The results and puzzles are below.

There are some interesting things to notice.
1) For some of the puzzles, the rating goes up as more techniques are added.
2) Look at the ratings for the "Discrepancy" puzzle ! (8th line)

Best Regards,
Blue.

Technique sets:

Code: Select all
`     s -       Naked and Hidden Singles, and line of sight eliminations   lcs - adds: Locked Candidates (Pointing, Claiming) lslcs - adds: Locked Subsets (Naked and Hidden Pairs, Triples, Quads)flslcs - adds: Basic Fish (X-Wing, Swordfish, Jellyfish)`

Ratings:

Code: Select all
`     T  |       s       lcs    lslcs    flslcs | puzzle--------+--------------------------------------+------------------------------23.2402 | 150.7094  123.7298  82.3268  81.7341 | GoldenNugget22.6372 | 147.6405  123.2902  85.7411  84.6015 | Kolk22.340* | 145.6346  125.0115  85.0152  82.0809 | Patience22.1194 | 139.1479  108.1807  77.7374  77.3910 | Imam_bayildi21.585* | 145.5524  117.0809  79.7549  79.1427 | Second_flush21.067* | 124.8864  105.3040  80.4641  79.6359 | champagne_dry20.1075 | 119.9944  100.2021  74.2189  73.4845 | eleven21219.9646 | 169.4545  140.5230  90.8898  90.7095 | Discrepancy15.6924 | 128.6754  109.7834  81.5317  80.0423 | Red_Dwarf15.5665 | 143.1666   82.7591  45.6534  44.1998 | AI_WorldHardest:Everest(2012) 9.9724 |  51.6346   44.3559  37.7688  37.3271 | AI_WorldHardest2006Escargot 9.9724 |  30.8243   28.7598  24.7899  24.6144 | AI_WorldHardest2010 4.6867 |  65.1211   29.0808  14.7689  14.7689 | 17Hints35410 4.2386 |  76.9150   48.0631  15.5645  15.5644 | 17Hints35409 3.4250 |  67.5199   36.8486  43.8726  44.5805 | 17Hints2919 3.2352 |  18.1570   15.1152  15.0943  15.5510 | 17Hints41826 3.1609 |  25.7975   12.9399  15.1081  15.1152 | 17Hints48126 2.7083 |  64.6332   52.6721  34.4980  34.4389 | JapaneseSuperComputer322 2.7000 |  85.6295   42.8059   5.5976   5.5977 | 17Hints35043 2.5700 |  19.1333    9.0256   9.0112   9.0050 | 17Hints41164 2.2500 |  69.6821   43.1810   4.4054   4.4054 | 17Hints35045 2.0222 |  32.7034   17.1254   6.3354   6.3201 | 17Hints24147 2.0167 |  35.3365   17.8776   6.6121   6.6149 | 17Hints35044 2.0000 |  32.8204   19.2850   3.7818   3.8396 | 17Hints35042 1.9286 |  11.2696    7.9510   8.2605   8.2269 | 17Hints28653 1.8500 |  26.7631   17.5557   9.2713   9.2733 | 17Hints24153 1.8000 |   7.2228    5.5842   5.5918   5.5534 | 17Hints18573 1.7727 |   8.9374    5.7402   5.3602   5.1533 | 17Hints42464 1.7619 |  12.4693    7.0411   7.3569   7.3569 | 17Hints41972 1.6875 |  15.5855   14.2533   5.0847   5.0863 | 17Hints32733 1.6667 |  17.3935    7.4061   9.7625   9.7596 | 17Hints33052 1.6667 |  20.5692    7.9810  10.8056  10.8020 | 17Hints4934 1.6500 |  13.9067   12.9607   9.3619   9.3542 | JapaneseSuperComputer313 1.6351 |  35.1865   21.1222   3.1004   3.1001 | 17Hints41750 1.6000 |   5.4854    5.3650   5.3650   5.2066 | 17Hints12538 1.5000 |   8.8403    4.4944   4.4944   4.4944 | 17Hints12995 1.5000 |   7.1596    5.4240   5.3995   5.3995 | 17Hints21752 1.5000 |   6.9403    6.7366   6.7533   6.2380 | 17Hints26041 1.5000 |   8.1493    6.5542   5.5294   5.4891 | 17Hints39923 1.5000 |  17.7356    4.0557   4.0557   4.0557 | 17Hints40086 1.5000 |  88.9682   28.3550   1.5000   1.5000 | 17Hints44580 1.5000 |   6.2596    5.1312   4.9402   4.9401 | 17Hints47137 1.5000 |   6.3676    4.6196   4.9621   4.9492 | 17Hints48498 1.5000 |   3.9583    3.9658   3.9725   3.9673 | 17Hints8780 1.5000 |   3.1147    3.0647   3.0647   3.0647 | 17Hints9404`

Puzzles:

Hidden Text: Show
000000039000001005003050800008090006070002000100400000009080050020000600400700000
120300000400000300003050000004200500000080009060005070001500200000090060000007008
120300000405000600070000020600100300004530000000008009000450100000000080000002007
003006080000100200000070004009008060030040001070200000300005000005000600980000050
120030000400001020005200100500400200000060070000003008050000900009070030000008006
980700000700000600006050000040005030007900500000020001008500900000010004000003020
100000009006700020080000400000075030005002000060300000090000800600040001002500060
120400300300010050006000100700090000040603000003002000500080700007000005000000098
120300004350000100004000000005400200600070000000008090003100500000009070000060008
800000000003600000070090200050007000000045700000100030001000068008500010090000400
100007090030020008009600500005300900010080002600004000300000010040000007007000300
005300000800000020070010500400005300010070006003200080060500009004000030000009700
602050000000004030000000000430008000010000200000000700500270000000000081000600000
602050000000003040000000000430008000010000200000000700500270000000000081000600000
000010600300000020700000000000702000010000800500300000000200035400000007060000000
050600000000000730000100000000070800060000050100000000700040200004030000000500060
140070000000200050030000000605000100800000700000300000000500023000014000000000000
080000150406509080000008000000000000002040003300801000900070000600000004150000090
600302000040000010000000000702600000000000054300000000080150000000040200000000700
006070040050000200000000000520000100000040000000600000000302500708000060000001000
600302000050000010000000000702600000000000054300000000080150000000040200000000700
083400000000070050000000000040108000000000027000300000206050000500000800000000100
600302000040000080000000000702600000000000054300000000080150000000080200000000700
600302000010000050000000000702600000000000084300000000080150000000080200000000700
300000008000020400005000000020048000501000030000000000640000200000300070000100000
083600000000070040000000000060108000000000027000300000402050000700000800000000100
040000031500720000000000000000000260030001000800400000002060700000003400000000000
600000170000300002100000000000017600020000030000000000030200005000460000000000800
500006400000300000000000000002040800030250000090000000700004000100000020000000039
500170000030000200000600000000024800100000000000003000028000000004000006000700050
500630040102000700000000000030000060000001000000070000000800200040300000000000108
000051000040000030000000000070430600500000102000000000200800000000300070108000000
200007050000000300001208000700003001002000060060001400004106008008000700050000090
400020000000060080000100030000004500003700000010000000500000206000307000000000400
000900032901800000000000040030002000600000100000040000020080000000700600700000000
001070000000030500000000002000800610520000000000000000750600000000005001400000070
061000800000390000000000000089001000500000003000000020200430000000200060000000100
104000200600500030000000000030000058200014000000000000000020100050800000700000000
003000007000500010080000000000800300060400000100000000500037000000020600002000800
000600310002004000050000700090810000000000002000000600306700000000000090200000000
000300710006050000000000000000107300085000000000400000060020008700000400100000000
004000530080060000000010000100500700200000006000008000030400080600100000000000000
040000005000002000000080000000050080030700000000000100208000600000400720300500000
000350400600000200010070000070010050200400000000000000000000071400200000800000000
000420006010000000000600000000060310400705000000000000000031050206000000000000800
blue

Posts: 821
Joined: 11 March 2013

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

To b]denis_berthier, Jason and blue, Thank you very much for your post.
denis_berthier and Jason
denis_berthier wrote:I could see the consecutive spaces when I edited your post, but not in my browser (if you type consecutive spaces in html, it can "see" only one of them).
In html, you should use "&nbsp;" instead of spaces, but I don't know if the software of this forum accepts this.
If you type no-break spaces (alt-space) instead of mere spaces, I think it will work. (It works on my Mac.)

JasonLion wrote:Using the code tag is the best way I know of to show things where the spacing needs to be controlled. The UTF version of non-breaking space (alt-space) does work, but with a variable width font it doesn't always work out well in practice (depending on what you are trying to do). It adds extra space just fine, but you won't be able to line things up except at the start of the line.

For Japanese (and Chinese and Korean), most simple way is
to use CJK space character "　" like this "　　　　　　".
In any way, I had to check by "Preview" before "Submit".

denis_berthier
denis_berthier wrote:I wouldn't be so affirmative. Even if there is some confluence problem, we can't be sure it is the cause of what you see in this particular example.

Without knowing your chain rules precisely, I can't say much. Many sets of chain rules have the confluence property: reversible chains (xy-chains, AICs,...) and non-reversible ones (braids, g-braids, ...). Other sets don't: whips, g-whips,... (but, as I said before, effective occurrences of problems are very rare). Also, you spoke of "vectors"; I never heard of such a technique.

Please wait for few days. I will report after checking rating log.
I try to describe vector-based rules r14 & r15, in English.
It is based on "Off Off Vector" between two candidates.
"Off Off Vector" from Ca to Cb indicates "If Ca is not the big number, then Cb cannot be the big number".
The process of r14 is as follows.
[1]Get "Off Off Vectors"s by following processes
(1-1)If there are the strong link between Ca and Cx, and the strong/weak link between Cx and Cb,
"Off Off Vector" is defined from Ca to Cb.
(1-2)After Ca is eliminated, r7(Locked Candidates), r8(Naked Pair/Triple/Quad) and r9(Hidden Pair/Triple/Quad) is applied separately. If Cb is eliminated by any oh these application, "Off Off Vectors" is defined from Ca to Cb.
[2]Make network(s) by all "Off Off Vectors"s
For each connected component of the network(s),
for each node (candidate: denoted as Cｆ), test [3}
[3} CS(Cｆ) is defined as a set of all candidates Cr where exists a chained vectors from Cf to Cr.
If one of following contradiction condition is concluded, Cf is placed as the big number.
(A)all candidates(N) in a unit are included in CS(Cf), where N a certain number.
(B)all candidates in a cell are included in CS(Cf)
(My intention is a focused candidate(Cf) and a reached candidate(Cr).)

r15 uses "On On Vector"s, which are gotten by reversing "Off Off Vector"s .
Same procedure as r15 is proceeded.
If one of following contradiction condition is concluded, Cf is eliminated.
(A)2(or more) candidates(N) in a unit are included in CS(Cf), where N a certain number.
(B)2(or more) candidates in a cell are included in CS(Cf)
Followings are WEB page for explanation. Although explanation is in Japanese language, picture may help your understanding.In both picture, red lines are strong links.Green vectors are "Off Off Vector"s in r14, "On On Vector"s in r15.
r14:http://www.tknottet.sakura.ne.jp/Test/G8.html
r15:http://www.tknottet.sakura.ne.jp/Test/G9.html

denis_berthier
denis_berthier wrote:One way you can have an idea whether your set of rules has a problem with confluence is checking them individually for a stronger (but easier to check) property (stability for confluence): do you have a rule that can be applied in some case to produce an elimination of some candidate x, and such that no rule in your set could still eliminate x if another candidate y had been eliminated (or asserted) before? Needless to check this with the basic rules (Singles+locked-candidates+Subsets) we mentioned before (we know that set has the confluence property).

The only alternative approach I can imagine is, try to spot precisely where the divergence in your example occurs and to see what happens at that point in each case: which rule is applied or not, why it is applied in one case and not in the other, ... anything like that.

As I mentioned in above, I'm investigating what happens on two versions of Imam_bayildi.
After that I'll study on the confluence program of my T.
I suppose there are 2 problems of rule property. One is behavior on isomorphs, The other is behavior when candidate y was eliminated (as you mentioned). denis_berthier, would you kindly tell me the words for these? Are they confluence and stability ?

blue
blue wrote:I've coded your rating method, and tried it with some simpler versions of "T", on the puzzles that are currently listed on your web page.
The results and puzzles are below.

There are some interesting things to notice.
1) For some of the puzzles, the rating goes up as more techniques are added.
2) Look at the ratings for the "Discrepancy" puzzle ! (8th line)

Thank you very much for your very fast action.
Would you kindly rate following 3 puzzles?
coloin wrote: (Tue Feb 24, 2015 5:08 am)
I don't think you should forget about the Easter Monster puzzle where the sk-loop was first found or the Fata_Morgana or the puzzles with high Suexratt
Code: Select all
`1.......2.9.4...5...6...7...5.9.3.......7.......85..4.7.....6...3...9.8...2.....1#Easter Monster`

Code: Select all
`........3..1..56...9..4..7......9.5.7.......8.5.4.2....8..2..9...35..1..6........#Fata_Morgana`

Code: Select all
`..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..#Suexrat9-10364`

These may or may not score highly in your program - i am suspecting the suexrat9-10364 will

I found " the rating goes up as more techniques are added" around 17Hints35042.
But is it logically possible?
tknottet

Posts: 24
Joined: 15 February 2015

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

blue wrote:There are some interesting things to notice.
1) For some of the puzzles, the rating goes up as more techniques are added.

tknottet wrote:I found " the rating goes up as more techniques are added" around 17Hints35042.
But is it logically possible?

It may not be a bug in your code. If a candidate eliminated by the additional rules is one with the smallest "local rating" in its cell, the "local mean" for the remaining ones can be increased.

However, it raises questions about the rating.
denis_berthier
2010 Supporter

Posts: 1269
Joined: 19 June 2007
Location: Paris

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

Impressing work again, blue!

And yes, finding a number, which does not help, will longer the solution path - bad luck. But surprising, that this can make it worse on average.
eleven

Posts: 2064
Joined: 10 February 2008

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

Thank you eleven.

tknottet wrote:Would you kindly rate following 3 puzzles?

These were good choices on Colin's part

Code: Select all
`     T  |       s       lcs     lslcs     flslcs | puzzle--------+----------------------------------------+---------------   ?.?? | 858.9493  621.9575  678.4785  671.6468 | Suexrat9-10364   ?.?? | 338.0826  261.9336  174.8692  173.9067 | Fata_Morgana   ?.?? | 106.9735   97.9841   68.5982   66.7936 | Easter Monster`

===

blue wrote:There are some interesting things to notice.
1) For some of the puzzles, the rating goes up as more techniques are added.

tknottet wrote:I found " the rating goes up as more techniques are added" around 17Hints35042.
But is it logically possible?

denis_berthier wrote:It may not be a bug in your code. If a candidate eliminated by the additional rules is one with the smallest "local rating" in its cell, the "local mean" for the remaining ones can be increased.

However, it raises questions about the rating.

I'm pretty sure that it isn't due to a bug in the code -- which was my first guess.
I triple checked everything, and finally did a check on the math involving R(P1(C)) numbers, by comparing the results against "# of times T is applied" averages over 1,000,000 random resolution paths. The results from the two methods agreed (within "95% confidence" intervals). Also, the error estimates were small compared to the increase in ratings that I was seeing at the time.

I wouldn't quite say that it raises questions about the rating itself.
It is what it is, after all -- based on its definition as an expectation value over complete resolution paths that involve "guessing" and backtracking, and that play out according to perscribed rules ... a "resolution strategy".
However, it may raise questions about the wisdom behind the particular strategy.

What you said about the "local mean" for the remaining candidates be increased, is true of course.
The main effect, though, might be due to bi-value cells being produced, where none would exist with the smaller T, and that leading to a complete shift in the available choices for the "next guess" cell.
blue

Posts: 821
Joined: 11 March 2013

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

denis_berthier, eleven and blue, thank you very much.
I understood why the rating occasionally goes up as more techniques are added

blue, thank you very much for additional rating, too.
I want to know whether law of large numbers overrides this problem or not.
Would you kindly try completely random T&E?
It means that in every stage try(in resolution model)/calculate(in rating) all candidates.
It should be much time consuming rating.
Even for relatively not-hard puzzle, for example 17Hints32733, I want to know the results.
My low speed code on my PC does not permit to try it.
tknottet

Posts: 24
Joined: 15 February 2015

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

blue wrote:What you said about the "local mean" for the remaining candidates be increased, is true of course.
The main effect, though, might be due to bi-value cells being produced, where none would exist with the smaller T, and that leading to a complete shift in the available choices for the "next guess" cell.

Quite right. Any cell may come to participate in the rating.

tknottet wrote:Would you kindly try completely random T&E?
It means that in every stage try(in resolution model)/calculate(in rating) all candidates.
It should be much time consuming rating.

I think it should be much less time-consuming, because the process will be much shallower.

It may be the right place to remind that, even with the simplest T, if all the candidates are tried (instead of only those in cells with the minimum number of candidates), the maximum possible level is 2 (for all the known puzzles). With one condition: the candidates must be tried repeatedly and effectively eliminated at level 1 before going deeper (it means that some candidates may have to be tried several times). Otherwise, what you get is some mean number of partial-T&E phases (where each phase depends on how the candidates are chosen).
Notice that, with partial-T&E, i.e. without repeated tries at the same level, you have a kind of non-confluence phenomenon. I overlooked this when I evoked non-confluence earlier: it may also come from your "partial"-T&E procedure.

Independently of the above, I think it wouldn't be much more work to output a triplet instead of the mean: (min, mean, max) or (min, expectation, Max): meM
corresponding to (good luck, medium luck, bad luck) in the choices of candidates.
denis_berthier
2010 Supporter

Posts: 1269
Joined: 19 June 2007
Location: Paris

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

denis_berthier wrote:
tknottet wrote:Would you kindly try completely random T&E?
It means that in every stage try(in resolution model)/calculate(in rating) all candidates.
It should be much time consuming rating.

I think it should be much less time-consuming, because the process will be much shallower.

It may be the right place to remind that, even with the simplest T, if all the candidates are tried (instead of only those in cells with the minimum number of candidates), the maximum possible level is 2 (for all the known puzzles).

I'm sorry I made a mistake again.
"try(in resolution model)/calculate(in rating) all candidates" should be
"select randomly one cell from all cells(in resolution model)/calculate all cells(In rating)".
The former means breadth-first search, but what I intended is depth-first search involving all cells as a possible target.
Of course, which is better for rating breadth-first or depth-first maybe discussed.
tknottet

Posts: 24
Joined: 15 February 2015

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

tknottet wrote:
denis_berthier wrote:
tknottet wrote:Would you kindly try completely random T&E?
It means that in every stage try(in resolution model)/calculate(in rating) all candidates.
It should be much time consuming rating.

I think it should be much less time-consuming, because the process will be much shallower.

It may be the right place to remind that, even with the simplest T, if all the candidates are tried (instead of only those in cells with the minimum number of candidates), the maximum possible level is 2 (for all the known puzzles).

I'm sorry I made a mistake again.
"try(in resolution model)/calculate(in rating) all candidates" should be
"select randomly one cell from all cells(in resolution model)/calculate all cells(In rating)".
The former means breadth-first search, but what I intended is depth-first search involving all cells as a possible target.
Of course, which is better for rating breadth-first or depth-first maybe discussed.

denis_berthier
2010 Supporter

Posts: 1269
Joined: 19 June 2007
Location: Paris

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

blue wrote:The main effect, though, might be due to bi-value cells being produced, where none would exist with the smaller T, and that leading to a complete shift in the available choices for the "next guess" cell.

I should retract that statement. It seems to be very rare for intermediate puzzle states with no bi-value cells, to be produced.
I'm thinking now, that instead, when I added subsets into the mix, it caused a lot of naked pairs to appear in the intermediate ("T-quiescent") states. I think it's usually a bad idea to choose a "guess" cell in a naked pair, when other bi-value cells are available.

denis_berthier wrote:Independently of the above, I think it wouldn't be much more work to output a triplet instead of the mean: (min, mean, max) or (min, expectation, Max): meM
corresponding to (good luck, medium luck, bad luck) in the choices of candidates.

Good idea.
I think I could work a standard deviation into the calculation too, and output two pairs: (min,max) and (mean, std. deviation).
I'll work on that.

tknottet wrote:I want to know whether law of large numbers overrides this problem or not.
Would you kindly try completely random T&E?
It means that in every stage try(in resolution model)/calculate(in rating) all candidates.
It should be much time consuming rating.
Even for relatively not-hard puzzle, for example 17Hints32733, I want to know the results.
My low speed code on my PC does not permit to try it.

tknottet wrote:I'm sorry I made a mistake again.
"try(in resolution model)/calculate(in rating) all candidates" should be
"select randomly one cell from all cells(in resolution model)/calculate all cells(In rating)".
The former means breadth-first search, but what I intended is depth-first search involving all cells as a possible target.
Of course, which is better for rating breadth-first or depth-first maybe discussed.

I'll see how it goes, but I'm sure I'll run into to problems trying the highest rated puzzles.
I can try producing actual resolution paths too, and see how that works -- like the "1,000,000" paths I was using in my "bug hunt" (only fewer !).

Cheers,
Blue.
blue

Posts: 821
Joined: 11 March 2013

### Re: Puzzles Usage in a Presentation of a New Rating of Puzzl

blue
blue wrote:I'll see how it goes, but I'm sure I'll run into to problems trying the highest rated puzzles.

Thank you very much. I am interested to the highest rated puzzles more。
I was only anxious about the processing time, when I wrote "even for relatively not-hard puzzle".

denis_berthier
Thank you very much for explaining non-confluence phenomenon many times.
I did not understand it well. At last I understood it.
When I compared two solving paths of 23-clue version of Imam_bayild and its isomoph(Pa and Pc, I illustrated previously), I found that the rule r15 eliminates entirely different candidate in each case.
This is natural. Because r15(also r14 and chain rules r10-r13) works on only one pattern which found first.
Then the next problem.
denis_berthier wrote:do you have a rule that can be applied in some case to produce an elimination of some candidate x, and such that no rule in your set could still eliminate x if another candidate y had been eliminated (or asserted) before?

I'm afraid that each of r10-r15 has this bad property.
Because if y breaks link-chain or vector-chain, there is not a guarantee to be able to eliminate x.
In fact, at the above mentioned level, T founds a contradiction for Pc, but doesn't find for Pa.
That causes difference between two ratings.
It seems that I must add some apologize on my hardest sudoku list page.
tknottet

Posts: 24
Joined: 15 February 2015

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