## 17-clue and 18-clue Sudoku update

Everything about Sudoku that doesn't fit in one of the other sections
From the top of last page
coloin wrote:
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grid                 SF         SFB      Random 17 [number 1122]   Random

suexsf value        24.10       24.02        24.17                 24.42

number of 17s       29           3             1                     0

number of 18s*     2076 [71]   240  [80]      89  [89]            1 [estimate]
number of 19s*    75211      10089          4182                 80 [estimate]

where * is the number of puzzles generated using a "backbone" of the grid - there may well be many more 18s & 19s.

I "suexmulted" 2076 .......an average of 71 per each of the 29 17s in the SF.......a considerable number of these will be non minimal. [approx 1500]. There may well be others.....even some from another "region" of the grid.

............................................................................................................................................
.
A little furthur thought on the maximum number of disjointed unavoidables.[two disjointed unavoidable sets dont have intersecting clues]

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The reason that I think the largest minimum clues is 20 is that it is impossible to construct a grid which has more than 20 disjointed sets. You would have to have 20 disjointed 4-set unavoidables. It is also likely that a grid with 16 disjointed 4-sets, which has only room for 2 more disjointed 6-sets, will be solvable in 19 clues.

I mentioned that the upper limit numerically as 20 - in a way proving that it wasnt impossible to solve any sudoku in less than 21 clues.............

But it seems that it may not possible to fit more than 16 4-set disjointed unavoidables in any grid - and even that is going to be difficult.......with these 16 4-sets there will not be any room for any other disjointed 6-set.

Moschopulus wrote:I doubt very much if any grid has MCN = 17.

I think Mosch understood this but didnt say why !

This makes it even more likely that almost all grids are solvable in 18.

I will "try" to construct one of these high MCN grids to demonstrate..........

EDIT

Some grids with MCN of 15 and 16 have been posted recently
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MCN -15  [all clues in a 4 set ]
123568479864791352957243681218657934536489127749312865391825746472136598685974213

MCN -16
145726983837495261926381574293874156581269347674153892318547629459632718762918435

I doubt they can be done in 20 !

EDIT They both can be done in 20 [but almost certainly not 19]. See http://forum.enjoysudoku.com/viewtopic.php?t=2524
Last edited by coloin on Fri Dec 16, 2005 8:55 am, edited 2 times in total.
coloin

Posts: 1877
Joined: 05 May 2005

### Re: 17-clue and 18-clue Sudoku update

Lardarse wrote:In SF where you found 29 (iirc) minimal 17's, how many minimal 18's are there?

As far as i remember i didnt find a region with 18-clues apart from the 17-clues when i searched the grid, but i did not try for a long time, cause the 17s were found relatively soon for my method (after 1 day).
[edit:]This is only an answer to coloins question. of course there are some non trivial 18 clues in the 17-clues region, but i dont know how much.
Wolfgang

Posts: 208
Joined: 22 June 2005

Some interesting data just arrived...

I was sent, from Japan, a number of new 17-clue Sudokus. He or she (I can't tell from the name!) had constructed 700 puzzles, of which 33 were not already on the list.

So, maybe this means that we really DO have almost all the 17s..

How to prove it though is entirely unclear...

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

gfroyle wrote:Some interesting data just arrived...

I was sent, from Japan, a number of new 17-clue Sudokus. He or she (I can't tell from the name!) had constructed 700 puzzles, of which 33 were not already on the list.

So, maybe this means that we really DO have almost all the 17s..

How to prove it though is entirely unclear...

Gordon

did he/she use a method different to yours ?
dukuso

Posts: 479
Joined: 25 June 2005

dukuso wrote:did he/she use a method different to yours ?

Almost certainly yes, but I do not know details.. I will encourage him/her to tell me and/or join the forum...

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

Here's another pseudo-puzzle with 16 clues and 4 completions:

000010400800000060000900000041050000000000083000000000200806000060000100000300000
Moschopulus

Posts: 256
Joined: 16 July 2005

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000010400800000060000900000041050000000000083000000000200806000060000100000300000

is equivalent to this one from gfroyle's list:
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5.42.........4..3.1.........6..73.........5.1..........3.....7....5..4..8........
Wolfgang

Posts: 208
Joined: 22 June 2005

How do you tell if two puzzles are equivalent?
Moschopulus

Posts: 256
Joined: 16 July 2005

Moschopulus wrote:How do you tell if two puzzles are equivalent?

http://forum.enjoysudoku.com/viewtopic.php?t=2505
Wolfgang

Posts: 208
Joined: 22 June 2005

I wonder that i didnt find this 17-clue in the list, there are 23 others around, which i all found in the list (maybe a bug?):
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120900000500000000000040300700001000008000400000000900004030070000005020000000010
Wolfgang

Posts: 208
Joined: 22 June 2005

Wolfgang wrote:I wonder that i didnt find this 17-clue in the list, there are 23 others around, which i all found in the list (maybe a bug?):
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120900000500000000000040300700001000008000400000000900004030070000005020000000010

this puzzle is equivalent to
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....4..82631..................1.76..8......5....3......7....1..4...8.......2.....
gsf
2014 Supporter

Posts: 7306
Joined: 21 September 2005
Location: NJ USA

Thanks, so i have a bug in my normalization program
[Edit:] Fixed it, will update the source on the website this evening.
Wolfgang

Posts: 208
Joined: 22 June 2005

### Re: 17-clue and 18-clue Sudoku update

coloin wrote:A question...
In the grids with 17 clues......are there any 18s in these grids which have only a small number[or none] of clues in common with the 17 puzzle ?

Lardarse wrote:I'll take that question 1 step further:
In SF where you found 29 (iirc) minimal 17's, how many minimal 18's are there?

with 14 common clues use suexmult.exe over this text file
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111121211121111111121111111111211112211111111211111211211121111111111111111112122
639241785284765193517983624123857946796432851458619237342178569861594372975326418

suexmult file.txt 3 4 = 29 [17 clue] sudokus found
suexmult file.txt 4 4 = 2076 [18 clue] sudokus found

.......a considerable number of these will be non minimal.

EDIT...using suexmu35.exe which is modified to only print or cont minimal puzzles
suexmu35 sf.txt 4 4 = 397 [18 clue] sudokus found
suexmu35 sf.txt 5 4 = 6316 [19 clue] sudokus found

these are minimal suduku puzzles with this 14 clue backbone.

but I chanced upon these other [18s] [all minimal] which cannot be in the list [they dont have the 14 clue backbone]
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..9.4.7...8........1.....2....8.7..6.........4.....2..3.2.7..............7...6.18
...24.....8........17.........8.79...........4.....2..3..1...6........7..7...6.18
...24.....8.7......1....6.....8.7...7........4.....2..3.2.....9.......7......6.18
....4.7...8.7.....51..........8.7..6.........4.....2..3.2.............7..7...6.18
....4.7...8.7.....51..........8.7............4.....23.3.2....6...........7...6.18
....4.7...8.7.....51..........8.7............4.....2.73.2....6...........7...6.18
....4.7...8.7.....51..........8.7............4.....2..3.2....6........7..7...6.18
....4.7...8.7.....51..........8....67........4.....2..3.2.7...........7......6.18
....4.....8.7...9..17.........8.7..6.........4.....2..3.2.............7..7...6.18
....4.7...8.7......1..........8....67........4.....2..3.2.7.5.........7......6.18
....4.....8.7.....517.........8.7..6.........4.....2..3.2.............7..7...6.18
....4.....8.7.....517.........8.7............4.....2..3.2....6........7..7...6.18
....4.....8.7......17...6.....8.7............4.....2..3.2.....9.......7..7...6.18
....4.....8.7......17.........8.79...........4.....2..3.2....6........7..7...6.18
....4.....8.7......17.........8.7..6.........4.....2..3.2...5.........7..7...6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.....9.......7..7...6.18
....4.....8.7......1....6.....8.7...7........4.....2..342.....9.......7......6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.21....9.......7......6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.7...9.......7......6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.....9......37......6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.....9.......7....3.6.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.....9.......7.....26.18
....4.....8.7......1....6.....8.7...7........4.....2..3.2.....9.......7......6418
....4.....8.7......1....6.....8.7...7........4.....2..3.......9.6.....7.....26.18
....4.....8.7......1....6.....8..9.67........4.....2..3.2.7...........7......6.18
....4.....8.7......1....6.....8....67........4....92..3.2.7...........7......6.18
....4.....8.7......1....6.....8.....7........4....92..3.2.7..6........7......6.18
....4.....8.7......1....6.....8.....7........4....92..3.2.7...9.......7......6.18
....4.....8.7......1....6.....8.....7........4.....2.73.2.7...9.......7......6.18

who knows how many more there are with the 10 common clues
Last edited by coloin on Tue Jul 25, 2006 6:58 pm, edited 2 times in total.
coloin

Posts: 1877
Joined: 05 May 2005

### Thumbs Up!

Wolfgang wrote:

I support it. It's the only thing that makes sense.
Haley430

Posts: 5
Joined: 19 December 2005

### Re: Thumbs Up!

hm, sense?
Wolfgang

Posts: 208
Joined: 22 June 2005

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