17-clue and 18-clue Sudoku update

Everything about Sudoku that doesn't fit in one of the other sections
ravel wrote:I called a set of puzzles a family with distance n, when all puzzles have a pairwise distance less equal n.

Similar to Gordon's idea above i also thought about clusters of puzzles, where a cluster of distance n could be defined this way:
1. Any set A with a single puzzle is a cluster
2. Set A remains to be a cluster of distance n, when a puzzle is added, that has distance less equal n to any puzzle in A.

I just posted n2-2007-05-23.dat.gz
which contains 3 fields
puzzle cluster-id gfroyle-ordinal
for a -gn2c neighborhood tour (size 2 neighborhood tour in my solver)
puzzles with the same cluster-id are in the same size 2 neighborhood

a size 2 neighborhood tour is similar to 2-off + 2-on except that off+on are done in pairs
and each pair must produce a valid puzzle
this does much more pruning that a pure 2-off + 2-on tour like havard is doing,
but the search space is a bit more tractable (-go2c for a pure 2-off +2-on in my solver)

I also added a hamming-style distance based on the sudoku space thread discussions
the distance is biased towards minimizing clue position differences first, then minimizing cell value differences

the -C option compares each pair of puzzles on the input (1 with 2, 2 with 3, etc.), lists the
distance, the first puzzle, and the second puzzle mapped to show a minimum distance mapping
ravel wrote:Now i wondered, what distance the cluster of known 17-clues has. To get a feeling, i looked at Ocean's puzzle
May 16, where he mentioned, that it does not have another 17 within 2 off/2 on. I found 4 puzzles in the old list
with the lowest distance 6 and 31 with highest distance 16.

that's a good idea
do a pairwise distance to find the min and max distance
in graph theoretic terms the max distance would be the diameter of the known 17 space
gsf
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Red Ed wrote:With all the great 17-mining that's been going on recently, I thought you might be amused by a method I have pioneered for not finding new 17s.

Interesting. Here is also a method that did not result in new puzzles: Find minimal neighbour puzzles to each puzzle in the set of known 17s, where neighbour puzzle is defined as below (all neigbours for unavoidable sets of size four found). Lots of puzzles found, also a fairly high rate of 17s, but no previously unknown.

ravel wrote:In the last time i had played around with "distances" between puzzles.

Maybe it is worth to mention an alternative kind of distance/closeness between puzzles...

Background: If we take a solution grid, locate an unavoidable set in that grid, and replace the unavoidable set with the permuted set, we get a new valid solution grid (normally non-equivalent, although they might be isomorphs). Let us call two such grids for neighbour grids. Similarly, let us call two puzzles neighbour puzzles if they are identical except for the clues that belong to one unavoidable set.

Here is an example where two 17s differ only by one (complete) unavoidable set:
Code: Select all
`000000000000000012003045000000000000000004360720010008100000000270000000000003400000000000000000012003045000000000000000004360270010008100000000720000000000003400.............................................xy................yx................`
(Of the puzzles with 17 clues, 66 have a neighbour puzzle that differ by a complete unavoidable set [counted one week ago]).

Another example: a puzzle with 20 clues that has a 17-clues puzzle as neighbour (and vice versa):
Code: Select all
`000000000000000012003045000000000000000004360270010008100000000720000000000003400 #M17000000000000000012003045000000000000000004360270010008100000000720003009000009403 #M20....................................................................x..y.....y..x`

Neighbour puzzles that differ by two clues:
Code: Select all
`000000000000000001002030000003000000000004015006007004040000000000080320050009800 #M17784192563635748291192536478473951682829364715516827934248673159961485327357219846 #G81784192563635748291192536478473951682829364715516827934258673149961485327347219856 #G81000000000000000001002030000003000000000004015006007004050000000000080320040009800 #M17.......................................................x.....y...........y.....x.`

In this respect, every puzzle has a set of neighbour puzzles for each unavoidable set in its solution grid. For an unavoidable set of size N, the neighbour puzzles of a puzzle with C clues can have from C-(N-1) to C+(N-1) clues.
Ocean

Posts: 442
Joined: 29 August 2005

More stats [40095 17s] :

The puzzles can be classified by number of digits in each type of unit.
For example here's a class (R=Row, C=Column, B=Box) :

R111222233 C111222233 B111222233

In the actual list [40095], there are 2000 classes.

Here are the 10 most popular ones :
Code: Select all
`                                                                                                   N              Distribution                                                            1184   R111222233 C111222233 B111222233                                                            1030   R011222333 C111222233 B112222223                                                             934   R011222333 C111222233 B111222233                                                             915   R111222233 C111222233 B112222223                                                             754   R011222333 C112222223 B111222233                                                             700   R112222223 C111222233 B111222233                                                             646   R012222233 C111222233 B111222233                                                             644   R012222233 C111222233 B112222223                                                             595   R011222333 C112222223 B112222223                                                             508   R111222233 C112222223 B111222233                                                                                                                     `

There are only 2 puzzles with 5 empty units (3R + 2C or 2R + 3C) :
Code: Select all
`100500607020030800000000000080000230500100000000000000030020040700000001000000000750000030000240000800100000010500200300060070000000000020000100600030000000000000 `

JPF
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gfroyle wrote:In the thread you mentioned, various options are given for the distance between two puzzles A and B. Now to my mind we clearly want to view a puzzle as representing the entire equivalence class of puzzles that can be obtained by permutations, rotations etc, and so D(A,B) must be invariant under replacing A by A' and B by B'. This means that you are basically forced to take D(A, B) = min { d (A', B') | A' ~ A, B' ~ B }. [This *does* satisfy the triangle inequality so it is a legitimate metric on the set of equivalence classes.]
Agree that any distance measure should be a metric on the set of equivalence classes.
In the case two posts above: Let D(A,B) be the distance between two grids (or puzzles). Let us set D(A,B)=1 for two neighbour grids (or puzzles), differing by an unavoidable set of size<=U (say U=4, or U=6, ...). Let D(A,B)=N if it takes N steps to go from A to B, using stepsizes of D=1. Open questions: If we start from a single grid, will a complete path/tour define a closed set, or will all grids eventually be visited? In case of a closed set, how many such closed sets are there? In case every grid is visited, what is the maximum distance between two grids?
Ocean

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Joined: 29 August 2005

JPF wrote:More stats [40095 17s] :

The puzzles can be classified by number of digits in each type of unit.
For example here's a class (R=Row, C=Column, B=Box) :

R111222233 C111222233 B111222233

In the actual list [40095], there are 2000 classes.

Here are the 10 most popular ones :
Thanks for the stats.

One immediate comment: If these two are defined as different classes, the classification of a puzzle is dependent on a specific normalization. If they are defined as one common class, the classification is invariant to normalizations:
Code: Select all
`700   R112222223 C111222233 B111222233508   R111222233 C112222223 B111222233`

And a second comment: It is also possible to define subclasses, for instance R011222333 can be 022-123-133, 023-122-233 or a number of other configurations. Similarly for the distribution of digits in boxes.
Ocean

Posts: 442
Joined: 29 August 2005

JPF wrote:More stats [40095 17s] :

The puzzles can be classified by number of digits in each type of unit.
For example here's a class (R=Row, C=Column, B=Box) :

R111222233 C111222233 B111222233

In the actual list [40095], there are 2000 classes.

Ignoring clue values, it's possible to create all isomorphs by swapping positions of rows **, positions of columns ** and possibly using a transpose. So isn't the box classification redundant

** band and stack restrictions apply
ronk
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Location: Southeastern USA

Ocean wrote:Maybe it is worth to mention an alternative kind of distance/closeness between puzzles...
When i see it right, my definition is a compromise between your definition of neighboorhood with unavoidable sets and the pure n-off/n-on distance. At least your samples have only distance 4 in my sense (like 2 off/2 on), while you would need 4 off/4 on (1 and 3) and 1 off/3 on for them.
ravel

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Joined: 21 February 2006

Ocean wrote:One immediate comment: If these two are defined as different classes, the classification of a puzzle is dependent on a specific normalization. If they are defined as one common class, the classification is invariant to normalizations:...

Thanks.
You are right.
I have to think about it.
I'm not sure that these new stats are very useful, except maybe the puzzles with 5 empty units.

JPF
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ravel wrote:When i see it right, my definition is a compromise between your definition of neighboorhood with unavoidable sets and the pure n-off/n-on distance. At least your samples have only distance 4 in my sense (like 2 off/2 on), while you would need 4 off/4 on (1 and 3) and 1 off/3 on for them.

Ok, thanks for comparing. I have no clear opinion about how to 'best' calculate the distance. Like the distance between two lakes: There is an objectively shortest distance. But a bird, a car and a fish would choose different paths between the two, and they would experience different path lengths.
Ocean

Posts: 442
Joined: 29 August 2005

No question, e.g. JPF and others had showed (meanwhile) many samples of puzzles, where changing only one given could change the difficulty of a puzzle a lot, i.e. from the solvers point of view they are completely different.

My definition of distance more comes from the question, which puzzles you can find fastest from a given one. And of course often there is some correlation of properties for near puzzles in this sense.
ravel

Posts: 998
Joined: 21 February 2006

Update...

Well, the 17-puzzles keep dribbling in from various sources with the incorporation of new puzzles to the database now automated... so at least this can look after itself. (Of course feel free to just email me puzzles if you find the script clumsy for adding lots of puzzles at once..)

http://people.csse.uwa.edu.au/gordon/sudokuid.php

It's a slow process ("an apple a day" did someone say?) but we're up to 40146 now; maybe Havard has a big clump that he hasn't submitted...

I'll add some more searching features for people wanting access to the DB, but very busy for a couple of weeks...

Gordon
gfroyle

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Re: Update...

gfroyle wrote:I'll add some more searching features for people wanting access to the DB, but very busy for a couple of weeks...

when you get extra time could you enhance the Identify Me! field to treat a <<81 digit
entry as a puzzle id number
thanks
gsf
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Location: NJ USA

here is another load not in the collection:

Code: Select all
`.8.6........12..........3..7....35......7....9.....6...3......7...9...1..5...8....81............4...9.2.....7...3..58....8..1.4........6..7..2...5..1..............81...2.....95..3...............18..5........39..........43..5..7....1..2.........9...24..5...6...7...1......2....8......3..6..1..........8..1..6.7......3.........9.1.....8......3....7......7....1.9....46............4.3....6....2..7..6.....5...9.5...6.....6...2.1.......4..3....7...9..1..3........2...4..........45.......9...924...........8...4...2...3..58...........9.1.6.........9...2.8...3.7............94...........7.....2......81............6.2........4.1...5.3..7..2..1.....94....1......4....6...5.....2.......4.16..8.3.........5.......7.8.2.3.4..............1........5........72.63..........4....75.....1....8..6....4...8..2...75........1...1.....36.3.....7.....8......84....9......1....2.5.....7...3.......4....8........51.....8......7.2..3.5.......8..2.....4.....1........3....1.8.5.......6..9..3.....1..6.3..........4.........75..9..3.....57....2......8.....2.1...48..........4....1..6......3....8.7................51.7.3.8......9.....5...2..4......73........6..1.28...........36.9.........45.3........4...........12.3....5..8..1.....2........1.5.........8..2..6.........2.3.9..........14.............47.....6...95.....1..6.1.6...........47..3........5..21.....7....8......6.......7.84.26......1..........1....4......9..5..............85.3..21........6.........8...42......1..63..7.....15..3..........7.2............7.8..........1....2....5..7...8......1.9...2.6.5...2......645..13........8.....4...83.....2...........1.....5...2..8......7..3......2.....7.5...8.1...8..............3.164..5............7....6..2..1....4....3......2.....87....1....3..............54.13...9...............643.....51...9...4.......2....84........3......6....8.....6....14........3..57......2.81.5.........3......2......1....3....4.6...........523...48......1...........4...5..738...........6..2..1..7..9..8...............53..6....6..4..........1.........2.1.49............56...3.1....6....58..............564..3......71.........7..1...3.....4.6..........22..4.3.....8...61........5.9.......4....1.........6...5..7....8...9..3.........6....5.3..........41.1..8.......6..57.1........9..4......74..........9.3...6..........6.3......9.8...7.........3.....6........4.1...2.....8.3..5........2.72.....1..2......5.54....6......1.......4...813.7.................1.....7...53.......6..3..2..6..8.......3...5........7.82.........4..1.........3.7...1.......5.2...1......52..6..8.......3...5........7.82.........4..1.........3.9...1.......5.2...1......52..6......4....8.7................21.7.4.8......9.....1...3..5......74........6..2.6...3.....5.1.............1.....547...2.....5.....8.....3.2...8.4.......4.......81...2.....95..3...............18..5........39..........43..5...6...1..2.........94...........7.....2......31............6.2........4.1...5.3..7..2..8.....94..........3..3.....76.1..8......84....9......1....2.5.....7...3.......4....8........51.....36.3.....7.....8......84....9.....1.....2.5.....7...3.......4....8........51..6......3....8.7............9...51.7.3.8............5...2..4......73........6..1..6......3....8.7...................7.3.8......9...155...2..4......73........6..2.....87....1....3..............54.13...9...............6.3.....51...9...4.6.....7....84........3......6....8.....6....14........3..52......2.81.5.........3......2..6..9.......3...5........9.82.........4..1.........3.7...1.......5.2...1......5..64.2...7......1..9..........2..4.91..5.....3.....8......1........3.6...4........57...4.....25...........8.....6.5.38...3....1...........1...2....8.4....3.........8.3.......5...1..7.......6..1.......4..78..5.....3......5.7..1..2......9...........2.....1.....4.....5.......6...1.2.5.......8..7.....341........4..8..7.....2....91.6......2...3.8......4...75..6...3..4.............24.......1.....9..........8.1.....6....7..3......8....6.......83.7.............21....2..1.......4..7..5.8..........76.1.2..............2......9....35........14...6.28.........4.1..7.....5...1....5......6..8..........4.3....7....1.2...7..5.....8...........4..3.2...2..1...1........3.9.......8....4.6.......9.......8..2..1....2..8.4......5..3..7.....1...12...8.....7....5............5...73.68......4........3..4.........8.6..7....2....1...92.....7....................16.8..4...........5.2....1..4.2...5.9..6.9.......1.2............4...8.3.5.....1.6...5......8....7........6..1.24...5..........7.....2...65..3.....1.......2.7.8...3..6.....4.....1.....25........1...3.......8.....183...5..2..9.7..............1.....7...2....9......4...9...2..6..4........8......1.5..........2.3........474.........78.........1..92....6..8..3...4..........1...14.........3..5...8......42.....7...9.....1.....4....3.....6.27....1.......8.....15.8...........39............6.1.7.3..9.......8...1...7.2.....94.............5...19.....4...27..............5....8..6...5.........921.7.4...3.....1.....2.........2.....5.....3.8..6..7......6...2.........3.1.1......93.8.1.......4...2..........92.....634...8.........1......6.....1.....8..8.9.......7.3.........9.4....6.......2.....634...8.....5...1......6.....1.....8..8.9.......7.3.........9.4....6.......2.....634...8.......9.1......6.....1.....8..8.9.......7.3.........9.4....6.......2.....634...8.........1......6.....1.....8..8.9.......7.3.........9.4...96.......2.....7.6...3...............398...........2...1..7...1.....8.3.4.7.6.........5...2....4.3...7.1.........5....763....1........8.6....5..3..4...........76..........2....5.9....61............8......6....2...3..9.5..8..6...3..1....7..2............2....84....7.3.............4.82...........31.....6...7...8.2..5.1......3.........2....84.5..71.............1....4......6..3.......3..8....7..15.38................2..8.3.7.......1.64.......1.7.....5....2....5..............284...1.5............8.1...9.......6......42........5.12.3....7..........4.64......7...1.....7.........21....6....8.53............6...2.........4.8.....9...8..41....3..7............2..265.........4..1......8...71.....8....6.....4...7.......3..2.61..............5...3......4....7.6......1....65.2............81......7..1..4.9......3...2.7.........3.....87...45.....1.......4.......25..3.8.....81...........43.6...2..............3....71.....2.......4.........57...6......8.....3....8..6...........3.22..9..5...3..7.......4....1..2...6..4..6.1.........97....8.........2..3.6........1.......7.3.1.....8.....4........2.....65.7..1.93.....2.........6......1.....28......4.....3........19.....3....2....7.....45.....31...2........4..8......6.5..3........9...31.........2...6....5.....2..65.....4....8........3......1..2.....387...9........34...5...9.82......5......1..6............43....7..8......4...8.....6......3.....35.......4..........9..1......4..389.6.....5............2.97........46....5......384............21.........6...2..7...93..85..........7...1.......9..3..2.........4....2.....57.3.........6.3.1...........4.8.5.......1.2....5.7...6........1...........6.9.....71.....5........24..5.9..6.....1.........5...1.......8.3....2....4..4...75.8....2..........3.......84..1.2......7........6..1...2..5.3............1..4..1..........6.2..........7.....145..6.3......8.....6.9...3..2.....1.....2......7..6.......5....2.......1.5..1.2....3....7.....8.........346.7......4..2.........4..83...1.....2...........5.12.............8....5..3.2...7.5.....1..9...8........4.....6........81....7.......64.2....37.....1.........6.5.1....5....7..........3.4.76..........52....1...3.3...2............1......4.....4..7....3..1...2.8.......41.............23.........2..8.9.........4.....2.........7.5......4.16.87.9......41..5........76......8...........438...2...........512.....9.....1.4........6....426..........21..............74....3.....5...1.2.....1...85..........479.........426..........21..............74....3.....5...9.2.....1...85..........479.........43.....7...1...5..9.......8..5...2....73..........9......4........694..1............5...1.4........5..2.........463.....18...............6..35.2.....7..1.8.......5......4...8..9...........1.6..72...3..5....8..........934...........3........57.5....1...2..6.........7.......5.42.3..1.....7......6.8....2......4...5.......6..5.....6.....12....3...7....73............5.9........1....8..5...1.4...........3.6.5...24...1.............2.....7...1.6.......8...8........15..7.4..3.....2.....6...5..4........1..4...3...6..1......97..26........3........8....249.......7.........5..83...6.2...............1..4....7...6......3..5....4..2...........83.......59....2...8.6..5..7.........1.....136...28..........8....1.3..........4.......7..5...5.6...........4...13......4..5..2....7.......6.3............312...1....9...7.....52..........9.4....1......8...6..7....1....5.......3....5.21..6...........4..2...53.........4..2.................15.6..8..............2....3..6.3..17.......5.4.2.54...........38.....6..2......7.34.6..2............5....15....2........3......7..5.....2.1...7.............3.....7.8...2.9......5......2....9..6..8...3.....4..6..5..3....1.....8...6.........274.......8..1...3..............324..1...........65..6......1...38.......5......9..62.........85..........6......7....4..3.91.2.......6.....1...7.9.................2.3...15.......46.........4.6..59.....8.....13.....6....1...2..7.........8..4....6.52.3..1.....1........9....3......4...6.......7....8.3.......5...1..7.........41..........78.95.....3......5.7..1..2......9...........2.....1.....4.....5.......6...1.2.5.......8..7......41........4..83.7.....2...1.....9....7..3...........6.......83.7..........8..21....2..1.......4..7..5.8......2...75..3.....1.......2.7.8...3..6.....4.....1.....25........1...3.......8...........5.......8.362.7......6...2.........3.1.1......93.8.1.......4...2...........2.....634...8.......9.1......6.....1.....8..9.8.......7.3.........9.4....6.......2....4.3...7.1.........5..7..63....1........8.6....5..3..4...........76..........2....4.3...7.1.........5....763......1......8.6....5..3..4...........76..........2....4.3...7.1.........5..7..63....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.....1......913..8.7................3.....94...2.....6..8......1..4.......7..8..2.....5.....9..1..3......8...........91...2.....43........5.....2.7.....5......43.....16.....9..1.38..........4..2...1.9...5......67.2.3..............87..6.1.................7..13.2...5......6.......3.8.2......1..4.........6.....6..52.14.................91.3...8......25.........7...2..6..1.6..3......5.........91...........5....8....9...1.........3........6..3..7..5..5......1.....9..2..2.8...9....36........7.....9...1...3.....4....7...3.5.2...7.9....5.......1......5..3.........8..2.4.........9.3..5....1..............72..8..3..4..5.......6..........14.6.7...6.....5........9.3..8....1..............72..8..3..4..5.......6..........14.6.7...6.....8.......9.....1...3..4.......5.....1.69..5......2..4...........4.....23...1..7..5..........7...1...3..4.......5.....1.69..5......2..4...........4.....23...1..7....5......9.....1...3..4.......5.....1.69..5......2...4..........4.....235..1..7...........7..1..3..5......2....3...6.8...5...4.4....1......2.....3.2.............8.......5.9.1.....2....3.6............6.4..3.....1.........2....28.....7..3...6......5....19.1.........3....4..........3.....6.1....92..74.........6...91....43.......5.....9.1.........3..7..........2.3.7........8..5......4..9.....19.6..7...5...8.............9..14..6......3.....2....82..3.9......5.6.....4.....4..6.........7..2...........9..1..428...............8.2..4..6...........3........4..3.71...6....9.....5......9..1..428...............8.2.74..............3........4..3.71...6....9.....2.....91....4......6..3.2...4.......1.964...7...8..........1...2........5.......6....9......1...4.23.....6.....2.3..........9..7.6.........1..7...84..3..2............9..1..........4.......8...7......1.4.65........2...7..89.........4..5...1...3....9..1..........4.......8...7......1.4.65........2...7..19.........4..5...8...3......1...42.57...............3..86....2..............5..41.....8......57.1....3.......1...42.57...............9..86....2..............5..41.....8......57.1....3.....91...4...8....23..............9...124...........6....3....2...5..3.7...........9.91..........6.8...........25....6.....91.......7...5.8.....3.....5....96......2.7.18........4...65......3......15....5.....3.....2....86.3.............1......2.........91.5..4......47........6..27.8..3.....1............89....7..1..........5.........91.5.4..............83..1.......6..5........4..1...89......5..6..2.......4.......915....8...............7..5....943.....2....8..6.....34.8..91....................915....8...............7..5....943.....2......86..3...4.8..91.................9.....5...37...1.......9.4.6..........35.......8..2......96.3.8..........1......9.1.....5.....3.7...6.4.....4..3.1.....2..9..............9...4.5......3..7.......9.....58.......3.....7..6...8...5..47............2...9...47.....5.....2.....9...91...........2.......6......6...4127..8....3........4...2.7....1.....9...9......91.............3....7...6....69.2..3......5.....7.....7....9.4...3..........51...91...5.....5...4..........38.7........4..91.......2..5....2.......9...34.........91.........6...4.......8....3.19.........2.7....3.6..68.2...........1..4.........91...5.....24..............6.4...3....9.1...7.......84.5.8....2...............9..915...........2.....3.....4...6.8......2.....5.1...9....9....58........2.....6..9.....5......3..........76..2.4.1....1.6...........3.....7.2.1.3.......95........9...1.......3...2.......6.....6..8.71....8.........4....64......8.....1..7......9.2.....916...4.............7.....63..8.9.1......8.....3...6.4...1..............2.........16.....2..4..5........7..85.21..........3.......7....4.....286...5...........9.1.86.........3.......2.......6...3...1.....1.....59...4.....6.27.....8.........91.........2.5.........3..5..6.4...2.......7....1....3.78...4........91..........91..632...........8.......7..3...91.............4.4..3.5...7..............8.9...9....564....................6.7...51..3.......2...47.....62....5........1..8.....1..6..3.4...5..75.......4...3..7.....6.8............862......2.....3...........91....6....3......2.......4.....3..5..6..7......9....34.7.........1..9.........2.1..........3..7...6.5......4.....1......8......7.....7.....5.6..2.1....3...4.8.........9.7..5............1..1.39....4.....7......1..2....8.74..29.............5.........9.7..5............1..1.39....6.....7......1..2....8.74..29.............5.........9.7..5............1..1.39....4.....7......1..2....8.7..429.............5.........9.7....5..........1..1.39....4.....7......1..2....8.7..429.............5...7...9..1....3.....2....6.....82..7.1..6.....9........5....1..7...4............2.....21..3.74...8...........6............4.3..1.........8.43.....5.7...1.........6...9..1..7...............5...81.....4......7.........2.19.7........52.4..3....8.....9..1..7...............5...31.....4......7.........2.18.7........52.4..3....8...6.1...7.5......3....2.....3...5..........1.8.....2....1....2.64.7.3..............9.1.87...3..........2.........3..654.....2........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Havard
Havard

Posts: 377
Joined: 25 December 2005

333 new ones, very impressive
I mischieviously entered your
Code: Select all
`5.....6.....12....3...7....73............5.9........1....8..5...1.4...........3.6`
into gordons database as number 40155........sorry !

I can guess that you [havard] has completed a full 2off/2on search of the existing 17s.

And from our communications you have abandoned the slow 3off/3on search method to the quicker and more productive 3off/2on search around various 18s [effectivly this is a 3off/3on search if the 18 is related to a 17.]

The 37 new 17s from the handmade 18 produced by Deano
Code: Select all
`6 . 5 | 9 . . | . . .. . . | . . 2 | 7 . 8. . . | . . . | . . .---------------------. 7 . | . 2 . | . . .. 1 . | . . . | . 5 .. . . | . 4 . | . 6 .---------------------. . . | . . . | . . .3 . 9 | 6 . . | . . .. . . | . . 8 | 2 . 4 `
was interesting in so much that there were no new 18s from my random 18.

Deanos 18 must be in a more remote area....is this effected by the lack of diagonal clues in 7/9 of the boxes ?

I am trying to think of ways to direct this.....

C
Last edited by coloin on Sun Jun 03, 2007 11:19 am, edited 1 time in total.
coloin

Posts: 1711
Joined: 05 May 2005

coloin wrote:
Deanos 18 must be in a more remote area....is this effected by the lack of diagonal clues in 7/9 of the boxes ?

I am trying to think of ways to direct this.....

C

Good point. If so this rectangular 19 might be great grist.

http://forum.enjoysudoku.com/viewtopic.php?t=4147&start=459

3 off 1 on is pretty quick I hope?
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006