## No new 17s within {-2+2}

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

### No new 17s within {-2+2}

Here in 2007 Havard reported he did exhaustive search for new 17-clue puzzles by removing 2 and adding 2 clues in all possible ways on the known at this time 17s.
I am confirming that there is no any unknown puzzle at {-2+2} around the currently known 49152 puzzles.

Cheers,
MD
dobrichev
2016 Supporter

Posts: 1785
Joined: 24 May 2010

### Re: No new 17s within {-2+2}

Are you sure are there 49152 currently known 17-clue valid puzzles? I loaded 49151 17-clue puzzles from Gordon Royle site several months ago. Has anybody really found new 17-clue valid puzzle last time?

I'd like to propose nuclear phisycs analogy for {-n+n} search. I think it is amusingly.

You know some nuclei of chemical elements are stable, but others - not stable. If a nucleus is not stable, it can decay to another nucleus and elementary particles. This process is called as radioactivity.

When we talk about sudoku we can imagine that collection of valid puzzle's cells forms nucleus. If puzzle is not minimal, we can subtract several cells containing clues from original puzzle, but transformed puzzle will still have unique solution only. We can treat such cells subtraction as radioactive decay - original nucleus emits another simple nucleus having several nucleons (cells). The final state of the nucleus (puzzle) is stable, because no nucleons (cells) can be emited (subtracted).

Searching for other valid puzzles within {-2+2} resembles me nuclear reactions, when 2 nuclei are colliding each other. If there is 1 way only to get minimal valid puzzle after adding 2 cells with clues - to subtract these extra cells, we can talk about elastic scattering. A nucleon hits another nucleon and they form common nucleon "cloud". Subtracting extra cells implies emitting of colliding nucleus. Elastic scattering is not interesting. But if it is possible to subtract some cells (not extra cells) of original puzzle preserving its validity, we can talk about inelastic scattering, i.e. about nuclear reactions.

Your search results imply that known 17-clue nuclei (puzzles) are very stable (minimal). No inelastic scattering was observed.

Serg
Serg
2018 Supporter

Posts: 717
Joined: 01 June 2010
Location: Russia

You can find the 49152th 17 puzzle here.

Code: Select all
`........1.....2.....3....45....463....5.......4...1......7...3..1.5.....8.....2.. # 49152 `
Afmob

Posts: 130
Joined: 28 June 2011

### Re: No new 17s within {-2+2}

Check for this puzzle in you DB
Code: Select all
`........1.....2.....3....45....463....5.......4...1......7...3..1.5.....8.....2.. # 49152 `

Edit: Afmob is faster than me.

I like your analogy with nucleus but there is one weak point - in the nature simple nucleus (hydrogen) are stable. Analogy is still applicable for high-clue puzzles. In order to get a stable configuration you need huge energy and the rest is matter of chance.
It is known that the most stable configuration is iron (Fe) but for some reason the portion of iron nucleus in the universe is extremely small. Maybe it is the same for the published puzzles since anomalies are always more attractive.

Back to the topic.
The existence of a black list with fruitless subgrids of size 15 hypothetically could help in some degree in some generation methods. For example if you do {-/+} at final stage, then knowing that your puzzle contains some of the blacklisted subgrids you know that you must touch this area, else you will eventually find already known puzzles traversing this "promising" and therefore large subtree. I have no idea how this can be done in computationally efficient manner.
dobrichev
2016 Supporter

Posts: 1785
Joined: 24 May 2010

### Re: No new 17s within {-2+2}

I would like to update my old list of the known 17 clues puzzles.

thanks

champagne
champagne
2017 Supporter

Posts: 7163
Joined: 02 August 2007
Location: France Brittany

### Re: No new 17s within {-2+2}

I uploaded the 17's list here.
dobrichev
2016 Supporter

Posts: 1785
Joined: 24 May 2010

### Re: No new 17s within {-2+2}

Hi, Afmob, dobrichev!
Thank you for news in 17-clue puzzles area.

For dobrichev.
Thanks for updated 17-clue puzzles list.
About idea of using {+n-m} search results in exhaustive search. The idea looks like crazy, but perhaps it has sense...

Serg
Serg
2018 Supporter

Posts: 717
Joined: 01 June 2010
Location: Russia

### Re: No new 17s within {-2+2}

dobrichev wrote:I uploaded the 17's list here.

thank you, I got it
champagne
2017 Supporter

Posts: 7163
Joined: 02 August 2007
Location: France Brittany

### Re: No new 17s within {-2+2}

From a recent post here

Serg wrote:
Code: Select all
`2 2 22 2 22 2 2`
............
If we filter out patterns having 2 empty rows (columns) in a band (stack), than we'll get 17,429,658 essentially different patterns.
Serg

thanks
some of those maybe wont have puzzles too ...... maybe not that many though

im not sure of the following with respect to 222222222-18s

and my guestimate is
average number of puzzles per pattern = maybe 50 -100
proportion of all 18-puzzles with this configuration - ? 5 - 10 % [cant see how to get a random sample easily]

1.6 billion 18s estimated total
80 - 160 million 18s with 222222222 box config. pattern

its pretty easy to generate these {-2+2} keeping within the box
either of
1. { -2 from one box +2 back in the box}
2. {-1 from 2 different boxes + 1 back in each box}

given the number of puzzles ......its too difficult for me to program and file

any non-minimals [17-puzzles] are easily found [they will be associated with 8 different 222222222-18s]

if you generated the total 2084 17-puzzles with 222222221 box config without a new one then i would say all have been found.

i generated over 300000 222222222-18s
in these there were over a 1200 222222221-17s
unfortunately none were new

C
coloin

Posts: 1921
Joined: 05 May 2005

### Re: No new 17s within {-2+2}

Code: Select all
`givens per digit222222221   10322222211   5299322222220   963332222111   16123332222210   12009333221111   3694333222110   9945333311111   24333321110   307422222111   37422222210   33432221111   181432222110   497433221110   30givens per box222222221   2084322222211   16764322222220   302332222111   17048332222210   1543333221111   4957333222110   1530333222200   21333311111   200333321110   195333322100   23333331100   1422222111   899422222210   115432221111   1901432222110   525432222200   4433211111   670433221110   265433222100   19433311110   13442211111   32442221110   24443211110   8443221100   3522222110   2532211111   1532221110   2533211110   1`

It sounds more promising to target the following two distributions
Code: Select all
`322222211   16764332222111   17048`
dobrichev
2016 Supporter

Posts: 1785
Joined: 24 May 2010

### Re: No new 17s within {-2+2}

Indeed

It would be a useful tool to be able to filter puzzles with {xxxxxxxxx} digit or [xxxxxxxxx} box distributions.

I was surprised that i got so many ~ half of the 17-puzzles with Box {22222221}.

I think i generated them with alternating {-1+1} and then a gridchecker --similar 2 on the new ones.

Would be a lot easier with the filter.

On the 300000 222222222-18s I am doing a complete {-2+1} {It will take 3 days} all the puzzles will be either
222222221
322222220
322222211

C
coloin

Posts: 1921
Joined: 05 May 2005

I claim #49153 .

Code: Select all
`........1.......23..4..5........6..5.4....7..12...........8.......12......63..4..   #49153`

I haven't done a {-n+n} search on it, so you might find other new ones.

Edit: As dobrichev pointed out this is not a new puzzle.
Last edited by Afmob on Mon Dec 03, 2012 1:13 pm, edited 1 time in total.
Afmob

Posts: 130
Joined: 28 June 2011

### Re: No new 17s within {-2+2}

Hi Afmob,

Unfortunately, your puzzle is a morph of this one, which is #38534 in rowminlex ordered collection of 49152.
Code: Select all
`........1.......23..2..4........2.5..3.......16....7......16......83......7...4..`
dobrichev
2016 Supporter

Posts: 1785
Joined: 24 May 2010

### Re: No new 17s within {-2+2}

You're right, dobrichev. There were some errors in my 17 database file.
Afmob

Posts: 130
Joined: 28 June 2011

### Re: No new 17s within {-2+2}

I was surprised to find this puzzle:
Code: Select all
`3........4.......8...2..1...1...56...2............4.3.95.....4....7........1....9 3 . . . . . . . . 4 . . . . . . . 8 . . . 2 . . 1 . . . 1 . . . 5 6 . . . 2 . . . . . . . . . . . . 4 . 3 . 9 5 . . . . . 4 . . . . 7 . . . . . . . . 1 . . . . 9  ED=2.6/1.5/1.5`

in yesterday's edition of Die Welt (Hamburg). I assume it's a morph of a known puzzle, but maybe someone could check?

Thanks,

Mike Metcalf

m_b_metcalf
2017 Supporter

Posts: 11218
Joined: 15 May 2006
Location: Berlin

Next