UAs collection using the brute force

This chapter covers the primary collection of unavoidable sets, one key issue  for  the search of 17 clues puzzles in solution grids.

This part of the code can be shared by the three programs to run in the “as of blue” mode..

The code used in the phase 1 (puzzles with one band / stack having more than 6 clues) was different.

More tests will be done on this code, but as it is, it passed the test of known 17 with the distribution 665, so it can be seen as safe (producing no false UA)

There are several ways to generate unavoidable set. In the proof that no Sudoku with 16 clues can be produced Gary McGuire used blue prints to find all unavoidable sets <= 12 cells in a solution grid.

Here, the generation is based on the brute force applied to “n” unknown digits, a process that I learned years ago from mladen Dobrichev.


In this document, to be understood by readers less familiar with the unavoidable sets issue, a detailed description of the way it appears in the 17 clues search is done in pages 2 and 3.

Pages 4 and 5 tell more about the code.


The following topics are developed here after :


2 UAs full grid, one band,2 bands

3 Gangsters Sockets and GUAs

4 UAs bands 1+2 generation

5 Sockets UAs primary generation