Less than one millisecond to tell whether a X+Y+27 puzzle contains a 17 clues puzzle.

If you don't believe it, you can have a look to the next posts

This is a problem we faced trying to see whether we are missing 17 clues puzzles in the 49157 known 17 clues puzzles.

There is no easy way to solve that problem. One feasible partial answer to reduce the problem has been to scan all solutions in a X+Y+27 pattern.

The negative answer for X+Y<8 came quickly. The X+Y=8 case is already much more difficult.

The "best known process" is split in four steps :

a) find ED patterns X+Y+27. This is a relatively short step

b) Generate valid puzzles against "gangsters", the minlex form of band1 possible starts with a given set of 3 digits in each column

c) expand these puzzles to any valid permutation within the columns

d) find in each of these puzzles the valid 17.

we consider here exclusively the last step. To give an idea of the "size", in the 4+4+27 case, we have 13 745 722 puzzles at the end of the step c).

Available programs at that time could find the 17 with a run time leading to a very long d) step, so we tried ("Blue" and me), to use the specificity of that case to have a faster process.

We have been lucky and arrived to a step d) processing the 13 millions puzzles in about half an hour (9500 puzzles per second)

The process applied introduce nearly no new idea, except one, the search of UAs of size 2;3.

The resulting code is very simple and summarize in a nice way some published concepts.

The reader is supposed to have a good understanding of the following :

Unavoidable sets and search of puzzles of size "n" in a solution grid

The oldest reference I know is the gridchecker program reworked by mladen Dobrichev gridchecker

The second and key reference it the work done by the Gary McGuire's team to prove that there is no 16 clues puzzle. Gary McGuire's article

The key concepts described in these references are supposed known by the reader.