[sfrank]

No, a domain-consistent all-different propagator such as the one desccribed in [1] is sufficient to determine a valuation domain for a Sudoku puzzle without any search.

Of course that does not hold in general, but in the special case of Sudokus and problem modelling by a domain-consistent all-different propagator, no search is required for a solution.

[1] A filtering algorithm for constraints of difference in CSPs, J-C. Régin, 1994

[taeric]

This thread exploded after I went to sleep. Apologies for the silence and again a huge thanks to everyone else in the thread.

It is possible to craft a sudoku that has a unique solution without having any forced moves at the beginning. Turns out most are not actually hard, but it is doable. When I get back near my book at home, I an post an example, if folks are interested.