JPF wrote:denis_berthier wrote:The original exhaustive search has been done long ago. What's underway is a replication of it (always good to have a confirmation of a result).
No.
The only exhaustive search was done for the 16s by Gary McGuire et al.
see hereThe current known 17s list is the result of many contributors work.
That list was initiated and had been maintained by Gordon Royle for a long period of time.
Most of the 17s found were the result of vicinity search. There is no evidence that the current list (49158 17-clue puzzles) is complete.
The work currently done by champagne et al. is an exhaustive search for 17s.
I should let
champagne explain the nature and the work he is doing on this subject.
JPF
Hi JPF,
The major findings in the 17 clues search are due to blue's work. He is also the finder of the last known 17 #49158.
In fact, thru deep vicinity search (last known by me is a +-3 vicinity done several years ago by mladen dobrichev with no positive result), the list of 17s is supposed to be nearly exhaustive, with a possible one or 2 17s missing.( 'against blue's estimate)
At this point, the only possibility to assess that we know all 17s is a full scan of the solution grids, similar to what Gary Mc Guire did on the 16 clues.
Blue proposed a new way to do this, but never disclosed the corresponding code, although he gave many clues in private messages on the strategy used.
I worked with him and started the scan with a first pass looking for 17s having one band or stack with more than 6 clues. The corresponding scan is over for years.
The last pass was to scan the solution grids for 17s having not more than 6 clues in bands and stacks.
This is the ongoing search, with an end expected by the end of this semester.
All this is heavily discussed
hereGary Mc Guire worked with 820 cores and it took him one year to establish that there was no 16 clues puzzles.
to-day, we have only below 40 cores dedicated to the scan, with I hope 15-20 more in the near future.
About 80% of the scan has been covered with no new 17.
To give more information in this field, "blue" still made huge progress in the search of low clues in solution grids.
Our friend "mathimagics", one of the contributor to the current scan (the possible newcomer is "mith") has a project to qualify solution grids having a 18 clues.
He has in hands a DLL from blue having amazing good results; Unhappily, again, we don't have the sources, and blue is not active to-day.
I am trying to crack the last ideas of blue, or to reached a similar performance. A true challenge.