The New Sudoku Players' Forum

[coloin]

Thanks ...... hopefully if we get that far that could be employed....if we get the majority by random methods ...
however I have to show first that grids with DB not completable in 12 clues exist !
[although there may be some merit in identifying those bands which are not completable in 11 [which there will be many]].
Those that don't have a plus 5 [so potentially have to have at least a 12plus6 ] dont have a 17C].

The first grid without a 21 [blue1]

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123456789456789123789123456214897365365214897897365214541632978632978541978541632


I have been generating random small puzzles from this blue1...... and there are no 12 completions so far...

blue did find a 12C in the MCgrid ... so indeed he has the methods !!

The MC grid has 6+6+27's:

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12...6......7....3.......5....5...9..64......8....1...312645978645978312978312645

which was a shame !

Edit: Grid1# renamed to blue1

[coloin]

This is the one to look at I think

Code: Select all

The first grid without a 21 [blue1]
123456789456789123789123456214897365365214897897365214541632978632978541978541632

Has it got a DB in 12 ?

[coloin]

Thanks for doing that ! ....
But it has scuppered it somewhat
Actually ........ you need to test all 6 DB

[coloin]

Actually I see that this grid is highly automorphic and is referred to as blue1, so it may well be that you have shown that all the DB have a 12-completion.
Your language is pretty good ... Thanks for your help

[coloin]

Yes thats excellent coding ....if no DB need 13 clues it is probably academic for the 17-search as you possibly have searched and excluded all grids with bands requiring 6 clues .

6 of the 416 bands have a minimum of 6 clues in band. (1;224;237;254;307;413 )
Any pair of these bands has a minimum number of clues of 12.
the best chance to pass 12 clues as minimum for 2 bands is with such a pair.....

I agree with that !
I'm a bit more optimistic now ....!

Previously published details on the 4 grids

Hidden Text: Show

Code: Select all

  1,  1,  1,224,224,224       0,     0,     0,     0,     0,     0       # 18                                 
  4,224,224,224,224,224     252,     0,     0,     0,     0,     0       #  6                                 
224,224,224,254,254,413       0,     0,     0,     0,     0,     0       #  6                                 
224,224,224,225,225,414       0,     0,     0,    90,    90,   324       #  2                                 
                                                                                                             
The bands that need 6 clues are  1,224,237,254,307,413                                                 

123456789456789123789123456214897365365214897897365214541632978632978541978541632 : blue1  puz20=0 puz21= 7488
123456789456789123789132465218967534564213978937548216391875642645321897872694351 : blue2  puz20=0 puz21= 3138
123456789457189326689327154216534897745891632938672541361245978574918263892763415 : blue3  puz20=0 puz21= 3894
123456789457189326689327154216534897745891632938672541392765418574918263861243975 : blue4  puz20=0 puz21=19682


Band numbers adjusted

[coloin]

Yes they are all big numbers .....
I an getting pessimistic to find a DB13 now, although it wouldn't be feasible to check all the potential DB.....
eg all 15 band pairs from (1;224;237;254;307;413 )

[coloin]

I think you have a good appreciation of the task - there is almost certainly DB which require at least 8 [4+4] clues but actually need 9.

983 Million DB ... how many pairs both with 6 clues needed.....

416 x 415 / 2 combinations = 86,320 pairs each equally likely perhaps [?] and we have 15 pairs both with 6 clues required

983 M * 15 / 86,300 = 170,000 pairs

MCN 16 grids might also be a good place to look .... but they may well be included in above ?
-

Another interesting thing about the grids is that only 187 (of the 222,278 found) have non-trivial automorphisms.

from this clever thread no grids with mcn >16

Addendum ... maybe its just not possible to put 13 UAs in 54 clues [cf the above thread] . Certainly not possible to put 13 disjoint U4s .

[coloin]

....
In the 17 search, we are considering ED bands 12 "minimal against the diagonal view"
This reduces the number of minimal in my case to 610 163 364 but using the 983,959,110 ED double bands would not be a problem....

"
Yes I didn't quite understand the .... " minimal against the diagonal view" .... but finally the penny dropped !!!
It must mean a diagonal reflection in a DB - which maintains equivalence - but the transformation is difficult to visualise !
I think that is a new one for most of us ... but well worth it !!!!

But maybe there is a bar set at 12 - [or it just doesn't exist] which might explain why you haven't found one in the more likely grids
[there is only theoretical space for 12 disjoint U4s in a double band - as there can only be 4 pairs per box][one spare clue per box]
But there are many non disjoint UAs which maybe just don't succumb to our 12 clues - especially with the bigger UAs which we never know about
and there are many possible band pairs for it to happen...

As with many things we try to achieve.... it is because its difficult that we try...
Proving something is impossible is just as valid as finding a needle in a haystack

[coloin]

Ok ...thats good they all need 12 clues ... and each DB expands to give approx 40 ED solution grids ...

maybe in those 100K DB ... there will be those which have a "ganster44reverse" pattern which isnt solvable in 6 clues ......

there are only 44 "gangster44reverse equivalents" or DBgangsters perhaps is better

this one produced fortuitously - from earlier post

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...........................123456789456789123789123456214897365365214897897365214   - none are solvable with 5

this might well be the only one of the 44 which isnt solvable in 5 / which needs 6 clues

All solutions of those DB which have that DB gangster all need 18C

but maybe those grids will just be combinations of our 6 bands (1;224;237/254;307;413) - and they are already excluded from your 17C search no doubt

Or maybe eg (1;224;237/xxx;yyy;zzz) (horizontal 3 / vertical 3) for example ..... that would be good because those solution grids could be excluded from your 17C search

[coloin]

maybe this explains .....

but maybe you knew this already !!!!!

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123456789457893612896127345634289157578631924219574863761345298942768531385912476 # {413 168 168  , 238 125 126}
 

This grid solution cant have a 17

Edited to another grid.
Program index416 attributes different band numbers. Band numbers needing 6 clues are { 1,132,145,168,202,413}
This grid has 3 bands which needs 6 clues. However minlexing it will hide it in the mix.

[coloin]

32 more solution grids which cant have a 17 ... and most lost in the minlexing

Hidden Text: Show

Code: Select all

123456789457893612896127345274689153638571924519234867761945238942368571385712496'413 202 202  , 316 399 344
123456789457893612896127345274689153638571924519234867961745238742368591385912476'413 202 202  , 382 180 305
123456789457893612896127345268319457714568923539274861971645238685932174342781596'413 202 202  , 275 234 361
123456789457893612896127345268319457714568923539274861972645138685931274341782596'413 202 202  ,  79 395  89
123456789457893612896127345234689157678531924519274863761345298985712436342968571'413 202 202  , 150 398  56
123456789457893612896127345274689153638571924519234867761345298985712436342968571'413 202 202  , 260 409  57
123456789457893612896127345234689157678531924519274863361945278942768531785312496'413 202 202  ,  49 372 354
123456789457893612896127345234689157678531924519274863961345278342768591785912436'413 202 202  , 377 397 107
123456789457893612896127345274689153638571924519234867361945278942768531785312496'413 202 202  , 260 401 364
123456789457893612896127345274689153638571924519234867961345278342768591785912436'413 202 202  , 408 397 118
123456789457893612896127345631278954574619823289534167742361598968745231315982476'413 202 202  , 395 235 149
123456789457893612896127345631278954574619823289534167745361298968742531312985476'413 202 202  , 407 374 269
123456789457893612896127345671238954534619827289574163742361598968745231315982476'413 202 202  , 396 366  65
123456789457893612896127345671238954534619827289574163745361298968742531312985476'413 202 202  , 412 303  50
123456789457893612896127345714268953568319427239574861971645238685932174342781596'413 202 202  , 342 200 304
123456789457893612896127345714268953568319427239574861972645138685931274341782596'413 202 202  , 129 409 282
123456789457893612896127345342689157678512934519374268231945876964738521785261493'413 202 202  , 382 225 216
123456789457893612896127345342689157678512934519374268931245876264738591785961423'413 202 202  , 408 194 235
123456789457893612896127345542689137678312954319574268231945876964738521785261493'413 202 202  , 192 338  50
123456789457893612896127345542689137678312954319574268931245876264738591785961423'413 202 202  , 192 403 264
123456789457893612896127345238569471574318926619274853961745238785932164342681597'413 202 202  , 395  93 248
123456789457893612896127345238569471574318926619274853962745138785931264341682597'413 202 202  , 299 291 317
123456789457893612896127345238579461564318927719264853971645238685932174342781596'413 202 202  , 392  77 156
123456789457893612896127345238579461564318927719264853972645138685931274341782596'413 202 202  , 228 386 120
123456789457893612896127345238569471574318926619274853741935268962781534385642197'413 202 202  , 385 193 333
123456789457893612896127345238569471574318926619274853742935168961782534385641297'413 202 202  , 409 323  75
123456789457893612896127345268579431534618927719234856971345268642781593385962174'413 202 202  , 410 126 237
123456789457893612896127345268579431534618927719234856972345168641782593385961274'413 202 202  , 354 354  46
123456789457893612896127345245689137678315924319274568531942876964738251782561493'413 202 202  , 208 341 120
123456789457893612896127345245689137678315924319274568782561493964738251531942876'413 202 202  , 208 341 120
123456789457893612896127345245689137678315924319274568782961453564738291931542876'413 202 202  , 342 171 155
123456789457893612896127345245689137678315924319274568931542876564738291782961453'413 202 202  , 342 171 155


[coloin]

I don't know why

I blame gsfs minlexing treatment

of course there will be an unknown number of DB which have a requirement to have 5+6 clues but actually need 12 ....
these DB could be treated similarly .....

I'm not suggesting for one moment that mathemagics and I generate 900M plus 5+6+12 puzzles from different grids ...

and of course testing a DB [on your part] for no 11 [ie must be a 12] is faster than testing for a no 12

[coloin]

Hi

I looked at those grids .... there is a difference in band labelling (1;224;237;254;307;413 ) which explains the confusion

It appears that index416 labels bands which need 6 clues as { 1,132,145,168,202,413}

But yes there are grid solutions with 3 bands of (1;224;237;254;307;413 ) which wont have a 17.

And testing those 224 combinations looks like the best chance

[coloin]

Well done for validating that .... as much as is possible .... and it makes sense as there really isn't room for 13 UAs in a DB....
The misunderstanding was in the labelling of the bands [although 1 and 413 were the same] and I have edited the posted grids.

[coloin]

as for example a distribution in box 222222222, something on which works our friend coloin.

Indeed I have been leisurely generating the extremes of the 18C . [ post forthcoming]. Indeed blue has estimated that these box-222222222 puzzles make up ~ 0.75% of all 18C
I think blue and Afmob independantly estimnated with a high degree of certainty here that there were about

Supersets method - Afmob - 1.9 billion 18C
Grid sampling method - blue - 1.91 billion 18C

Total grids with an 18C : (0.9683 +/- 0.0129) * 10^9 ~ 0.97 billion
60% of grids with an 18C have only one 18C puzzle ,

However it has to be accepted that the the initial generation approach is doomed to only find perhaps 95% of puzzles and never knowingly complete.
The problem lies in that there are many 18C puzzles which are {-2+2} remote of another 18C - so even if we could do a complete {-2+2} we wouldnt find these. Pretty sure thats why mathimagics has regrouped on the project !

Here is a 2-remote 18C

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+---+---+---+
|...|...|...|
|...|...|.65|
|...|...|.27|
+---+---+---+
|..1|38.|...|
|..5|...|8..|
|..6|..7|...|
+---+---+---+
|.4.|.9.|3..|
|.2.|...|...|
|.7.|..2|..6|
+---+---+---+


interesting in that it has empty box 1 and 2, and 4 clues in box 3

and here is ~90% complete list of 154 similar puzzles... which we can probably add most of these to the list

Hidden Text: Show

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................12.......34.....5.....1..3.....2..46...3..2.....8..6.7..45..9.... ED=2.0/1.2/1.2
................12.......34.....1.....5..6.....7..8.9..1..7...6.4..5.7...6..9.... ED=2.0/1.2/1.2
................12.......34.....5.....2..4.....9..36...4..1.....7..6.8..35..9.... ED=2.0/2.0/2.0
................12.......34..5...6....2..4.....7..8....8..5.....3..6.9...4.21.... ED=2.0/1.2/1.2
................12.......34.....15....3..2.....6..5....1..3.....5..4....27..8.6.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..24.....12.......43......7.9..5.. ED=7.2/2.3/2.3
................12.......34..1........5..67....4.28....2.1......3.4......9...76.. ED=2.0/1.2/1.2
................12.......34..1.....3..4..5.....6..78...2..1.....3..4.....9...87.. ED=2.0/1.2/1.2
................12.......34.....15....4..5.....6..2....1..3.....5..4....27..8.6.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..23.....12.......24......7.9..5.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..23.....12.......24......7.9..8.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..24.....12.......43......7.9..8.. ED=7.2/2.3/2.3
................12.......34.....1....5...67...8..43.....14.......42......7.9..5.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..43.....14.......42......7.9..8.. ED=2.0/1.2/1.2
................12.......34..1........5..67....4.28....2.1......3.4......9...78.. ED=2.0/1.2/1.2
................12.......34..1.....3..4..5.....6..78...2..1.....3..4.....9...85.. ED=2.0/1.2/1.2
................12.......34..2.....3..4..5.....6..78...9..2.....3..4.....1...85.. ED=2.0/1.2/1.2
................12.......34..2.....3..4..5.....6..78...9..2.....3..4.....1...87.. ED=2.0/1.2/1.2
................14.......39..9.....3..4..5.....6..78...2..9.....3..4.....1...87.. ED=2.0/1.2/1.2
................31.......94..1.....3..4..5.....6..78...2..1.....3..4.....9...85.. ED=2.0/1.2/1.2
................12.......343....1....5...67.......4...8.12.......43......7.9..5.. ED=7.2/1.2/1.2
................12.......34.....1....5...67..28...4.....12.......43.....7..9..5.. ED=2.0/1.2/1.2
................12.......34..1........5..87....4.2.....2.1......3.46.....9...76.. ED=7.2/2.3/2.3
................12.......34..1..5.....5..67....4.2.....2.1......3.4......9.7..6.. ED=7.2/2.3/2.3
................12.......34..1..5.....5..67....4.2.....2.1......3.4......9.8..6.. ED=7.2/2.3/2.3
................12.......34..1..5.....5..67....4.2.....2.1......3.4......9..8.6.. ED=7.2/2.3/2.3
................12.......34..1........5..67....4.2.....2.17.....3.4......9..8.6.. ED=7.2/1.2/1.2
................12.......34..1........5..67....4.2.....2.1......3.48.....9..7.6.. ED=7.2/1.2/1.2
................12.......34..1........5..67....4.28....2.1......3.4......9..7.8.. ED=2.0/1.2/1.2
................12.......34.....12...5...67...8..23.....1........24......7.9..5.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..23.....1...3....24......7.9..5.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..23.....1........24......7.9.85.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..23.....1........24......7.9..52. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..23.....12.......24.....7..9..5.. ED=2.0/1.2/1.2
................12.......34.....1...8....67..5...23.....12.......24......7.9..5.. ED=2.0/1.2/1.2
................12.......34..4..1....5...67...8...3.....12........4.....37.9..5.. ED=2.0/1.5/1.5
................12.......34.....12...5...67...8..23.....1........24......7.9..8.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..23.....1...3....24......7.9..8.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..23.....1........24......7.9.58.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..23.....1........24......7.9..82. ED=2.0/1.2/1.2
................12.......34.....14...5...67...8..43.....1........42......7.9..5.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..43.....1...3....42......7.9..5.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..43.....1........42......7.9.85.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..43.....1........42......7.9..54. ED=2.0/1.2/1.2
................12.......34..2..1....5...67...8...3.....14........2.....37.9..5.. ED=2.0/1.5/1.5
................12.......34.....14...5...67...8..43.....1........42......7.9..8.. ED=2.0/1.2/1.2
................12.......34.....1....5...67...8..43.....1...3....42......7.9..8.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..43.....1........42......7.9.58.. ED=2.0/1.5/1.5
................12.......34.....1....5...67...8..43.....1........42......7.9..84. ED=2.0/1.2/1.2
................12.......34..1..5.....5..67....4.2.....2.1......3.4......9..7.8.. ED=7.2/2.3/2.3
................12.......34..1........5..67....4.2.....2.18.....3.4......9..7.8.. ED=7.2/2.3/2.3
................12.......34..1........5..67....4.2.....2.1......3.48.....9..7.8.. ED=7.2/2.3/2.3
................49.......78..4..8.....12..5....9..7....8.......47..5.....6..3.2.. ED=4.5/2.0/2.0
................32.......14.....1....5...67..28...4.....12.......43.....7..9..5.. ED=2.0/1.2/1.2
................32.......14..1........5..67....4.2.....2.17.....3.4......9..8.6.. ED=7.2/1.2/1.2
................32.......14..1........5..67....4.2.....2.1......3.48.....9..7.6.. ED=7.2/1.2/1.2
................32.......14..1........5..67....4.28....2.1......3.4......9..7.8.. ED=2.0/1.2/1.2
................12.......34..4..1....5...68...8...3.....12........4.....37.9..5.. ED=2.0/1.5/1.5
................12.......34..2..1....5...68...8...3.....14........2.....37.9..5.. ED=2.0/1.5/1.5
................32.......14..1........5..67....4.2.....2.18.....3.4......9..7.8.. ED=7.2/2.0/2.0
................32.......14..1........5..67....4.2.....2.1......3.48.....9..7.8.. ED=7.2/2.0/2.0
................49.......78..4..8.....12..3....9..7....8.......47..5.....6..3.2.. ED=4.5/2.0/2.0
................49.......78..4..8.....12..5....9..7....8........7.65.....6..3.2.. ED=2.0/1.2/1.2
................49.......78..4..8.....12..3....9..7....8........7.65.....6..3.2.. ED=2.0/1.2/1.2
................49.......78..4..8.....12..5....9..7....8.56.....7........6..3.2.. ED=2.0/1.2/1.2
................49.......78..4..8.....12..5....9..7....8........7.65.2...6..3.... ED=2.0/1.2/1.2
................12.......34.....5.....6..28...79..1.......3.6..4...7....52..4.... ED=2.0/1.2/1.2
................12.......34.....1.....3..4.....5..67...4..8.....16.7....2...5.8.. ED=2.0/1.2/1.2
................12.......34.....1.....5..7....78..26......9.8..1...4...74...3.... ED=2.0/1.2/1.2
................12.......34.....1.....5..67...64..2....7..4.8..1...9....2...3.... ED=2.0/1.2/1.2
................12.......34.....1.....5..67...64..2...1...7....2...3.....8..4.9.. ED=2.0/1.2/1.2
................32.......14.....1....5...87..68...4.....12.......43.....7..9..5.. ED=2.0/1.2/1.2
................32.......14.....1....5...6...68...47....12.......43.....7..9..5.. ED=2.0/1.2/1.2
................59.......78..4..8.....52..3....9..7....8........7.65.....6..3.2.. ED=2.0/1.2/1.2
................43.......78..4..8.....32..5....9..7....8........7.65.2...6..3.... ED=2.0/1.2/1.2
................15.......74.....5.....6..28...79..1.......3.6..4...7....52..4.... ED=2.0/1.2/1.2
................15.......34.....5.....6..28...79..1.......3.9..4...7....52..4.... ED=2.0/1.2/1.2
................12.......74.....5.....6..28...79..1.......3.6..41..7....5...4.... ED=2.0/1.2/1.2
................12.......74.....5.....6..28...79..1.......3.6..42..7....5...4.... ED=2.0/1.2/1.2
................12.......34.....1.....6..7....75..26......9.8..1...4...74...3.... ED=2.0/1.2/1.2
................12.......34.....1.....8..69...64..2....7..4.8..1...9....2...3.... ED=2.0/1.2/1.2
................12.......34.....2.....6..58...79..1.......3.6..4...7....25..4.... ED=2.0/1.2/1.2
................15.......34.....5.....6..18...79..2.......3.9..4...7....52..4.... ED=2.0/1.2/1.2
................15.......34.....5.....6..28...39..1.......7.9..4...3....52..4.... ED=2.0/1.2/1.2
................13.......78..1..8.....32..4....9..7....8........7.65.2...6..3.... ED=2.0/1.2/1.2
................13.......78..1..8.....32..5....9..7....8........7.65.9...6..3.... ED=2.0/1.2/1.2
................41.......78..4..8.....12..3....9..7....8........7.65.9...6..1.... ED=2.0/1.2/1.2
................14.......263.1..5.....6..1...7....48...54.6........3.7......9.... ED=2.0/1.2/1.2
................15.......231....5.....2..1.....7..89......6.....9..2.7..58..3.... ED=2.0/1.2/1.2
................13.......56..3..6...2.6..5........49...9..2.8......3....57..1.... ED=2.0/1.2/1.2
................13.......56..3..6...2.6..5........87...9..2.4......3....57..1.... ED=2.0/1.2/1.2
................18.......56..3..6...1.6..5........27...9..8.4......3....57..1.... ED=2.0/1.2/1.2
................83.......259.3..6........5...8....2....2..9...6.5..3.....7..1.4.. ED=2.0/1.2/1.2
................18.......251.3..6.....8..2........5....2..1.....5..3..6..7..9.4.. ED=2.0/1.2/1.2
................15.......27..1..2.....6..38....51......2..9.3...7.56.....4....... ED=2.0/1.2/1.2
................16.......57..1........7..9.....56.43...9.7......6..1.....2..3.8.. ED=2.0/1.2/1.2
................15.......74.....5.....6..2....79..18......3.9..4...7....52..4.... ED=2.0/1.2/1.2
................15.......34.....5.....6..2....79..18......3.9..4...7....52..4.... ED=2.0/1.2/1.2
................15.......34.....5.....6..2....79..18......3.9..42..7....5...4.... ED=2.0/1.2/1.2
................12.......34...4.2.....6..5....7...18......3.6..4...7....25..4.... ED=2.0/1.2/1.2
................12.......34.....2.....6..5....79..18......3.6..45..7....2...4.... ED=2.0/1.2/1.2
................15.......26..3..69....8..7.....42.5....2..3.4..76...........1.... ED=2.0/1.2/1.2
................16.......29..8..2.....1..9.....5..43...9........7..6.....2.15.7.. ED=2.0/1.2/1.2
................18.......56.6...9.....2..37.......8...65..4.....9..2.4...1..7.... ED=2.5/1.2/1.2
................16.......73..1..3.....5.149....6.......7.25.....8.6......3....2.. ED=2.0/1.2/1.2
................48.......67.....65..1.8..7.....4..2....9..8...5....4.....7..1.3.. ED=2.0/1.2/1.2
................15.......69...8.5.....7..14....6......19..4.....5..7.2...8..2.... ED=2.0/1.2/1.2
................15.......69...8.5.....2..17....6......19..4.....5..2.4...8..7.... ED=2.0/1.2/1.2
................16.......23..1..3...3.5..49.......2.......1.8..49..6.....2..7.... ED=2.0/1.2/1.2
................31.......27..6..7.....8..2.7.9.4..5.......8.6..25..3........1.... ED=2.6/1.2/1.2
................15.......283.4..59.......8.5...7..1.....9.6.4......2.....8..3.... ED=2.0/1.2/1.2
................15.......283.4..59.......8.5...7..1.....9.6.7......2.....8..3.... ED=2.0/1.2/1.2
................18.......253.4..59.......8.5...7..1.....9.6.7......2.....8..3.... ED=2.0/1.2/1.2
................14.......268....5.....6..1...7....43.1.54.6........8.7......9.... ED=2.0/2.0/2.0
................15.......36...8.5.....2..1.....6...7..15..4.....3..7.4...8..2.... ED=2.0/1.2/1.2
................15.......96...8.5.....2..1.....6...7..15.3......9..2.4...8..7.... ED=2.3/1.2/1.2
................65.......21..8...9....51.7.....6.......1..8...2.7.49.....2..3.... ED=2.6/1.2/1.2
................62.......15..8.4.3....7..1.....5.......1....2...6..9.....2.73.4.. ED=2.0/1.2/1.2
................62.......15..8.4.9....7..1.....5.......1....2...6..9.....2.73.4.. ED=2.0/1.2/1.2
................65.......12..8.4.3....7..1.....5.......1....2...6..9.....2.73.4.. ED=2.0/1.2/1.2
................16.......57..1........7..9.....56.83...9.7......6..1.....2..3.8.. ED=2.0/1.2/1.2
................12.......94...4.2.....6..5....7...18......3.6..4...7....25..4.... ED=2.0/1.2/1.2
................12.......34...4.2.....6..5....7...18......3.6..4...7....25.1..... ED=2.0/1.2/1.2
................12.......94...4.2.....6..5....7...18......3.6..4...7....25.1..... ED=2.0/1.2/1.2
................48.......67.....69..1.8..7.....4..2....3..8...5....4.....7..1.3.. ED=2.0/2.0/2.0
................25.......183.4..59.......8.5...7..1.....9.6.4......2.....8..3.... ED=2.0/1.2/1.2
................15.......36...8.5.....2..1.....6...7..15...8....3..7.4...8..4.... ED=2.0/1.2/1.2
................51.......96...8.5.....2..1.....6...7..15.3......9..2.4...8..7.... ED=2.3/1.2/1.2
................12.......65..8.4.9....7..1.....5.......1....2...6..9.....2.73.4.. ED=2.0/1.2/1.2
................12.......36...2.5.....8..1.....6...7..15...2....3..7.4...2..4.... ED=2.0/1.2/1.2
................15.......23...8.5.....6..1.....2...7..15...8....3..7.4...8..4.... ED=2.0/1.2/1.2
................15.......36...8.5.....2..1.....3...7..15...8....8..2.4...6..7.... ED=2.0/1.2/1.2
................18.......23...8.5.....6..1.....2...7..15...8....3..7.4...8..4.... ED=2.0/1.2/1.2
................18.......36...8.5.....2..1.....6...7..15...8....8..2.4...3..7.... ED=2.0/1.2/1.2
................51.......26...8.5.....3..1.....4...7..15.2......9..6.4...8..7.... ED=2.3/1.2/1.2
................94.......28.....2...4.1..8........73..9.2.4.....7..1.5...3..9.... ED=5.6/1.2/1.2
................94.......28.....2...4.1..8........73..9.2.4.....7..1.5...5..9.... ED=4.5/1.2/1.2
................16.......27..67.4.....5.9.8....1.......4....3...7.25.....2..8.... ED=2.0/1.2/1.2
................19.......27..6..7.....8..54..97...2.......8.6..25..3........1.... ED=2.0/1.2/1.2
................16.......27..12.7.....5..9.....9..48..47...........5.3...2..8.... ED=2.0/1.2/1.2
................15.......36...8.5.....7..1.....2...7..95...8....8..2.4...1..6.... ED=3.4/1.2/1.2
................19.......87..4........1.2.3....9..7..6.8.15.2...7........6..3.... ED=2.3/1.2/1.2
................49.......28..4..6...1.3..87.......2....2..9.....7..4.5...8.1..... ED=2.0/1.2/1.2
................97.......24.7...58....2..1.....4..8...51..6........7..4..8..9.... ED=3.4/1.2/1.2
................15.......36...5.9.....2..1.....6...7..15.9......9..7.4...3..4.... ED=2.0/1.2/1.2
................67.......12..7.4.3....6..1.8...5.......1........8..9.....2.73.4.. ED=2.3/1.2/1.2
................17.......92..91.7.....6...5.......4....4.28.3...7..5....1...3.... ED=2.0/1.2/1.2
................65.......27..138......5...8....6..7....4..9.3...2........7...2..6 ED=2.0/1.2/1.2
................16.......72..12.7.....5..9.....9..48..47...........5.3...2..8.... ED=2.0/1.2/1.2
................18.......747.34.......8..9.....4..59...6..7.....1....5.....34.... ED=2.0/1.2/1.2
................16.......27..12.7.....59.......9..48..47...........5.3...2..6.... ED=2.0/1.2/1.2
................15.......36...8.5.....7..1.....2...7..95..4.....8..2.4...1..6.... ED=2.0/1.2/1.2
................19.......87..4........1.2.3..8....7..6..315.2...7........6..3.... ED=2.6/1.2/1.2
................67.......12..7.4.3..2....1.8...5.......1........8..9......973.4.. ED=2.6/1.2/1.2