Carcul wrote:[r1c8](-1-[r1c156])-1-[r146c9]-2,4,9-[r9c9](-6-[r9c34])-6-[r9c1](-8-[r9c5]=8=[r8c6]-8-[r1c6])-8-[r1c1]-7-[r1c6]-5-[r4c6](-4-[r4c9]-9-[r1c9]-2-[r1c2])=5=[r4c4]-5-[r9c4]-9-[r9c3]-2-[r7c2]

Correct me if I am wrong, but this looks like a one-direction implication network, which only means anything if you assume r1c8 = 1. I don't know if these other T&E definitions would admit such practices, but they would not pass my simple rule.

castalia wrote:It's unfortunate, but entirely understandable, that simple guidelines on sudoku often stress that solutions should be arrived at by "logic" and without the use of "trial and error". Well, any solution method that adheres to the rule of sudoku could be considered "logical", and even such simple techniques as singles could be considered trial and error (since "trying" to place that single anywhere else in the unit would violate the rule of sudoku and therefore result in "error").

I think you are right that if you adopt, or are forced into, a wide open definition of a trial and you are not allowed to make a distiction between a search for a relatively simple pattern versus arbitrarily assigning the content of a cell; then we should really be creating a thread about what we feel are acceptable procedures rather than what constitutes T&E.

Personally, I don't see why you can't make a distinction between these two types of trials. If you can't make that distinction, then how can you make a distinction between finding the puzzle vs solving the puzzle. In essence, the phrase, trial, represents everything, and thus becomes meaningless.

Bowing to the possibility I could be wrong about all I have written above, I will once again offer my simple rule for "non-guessing" vs "guessing" sudoku solving techniques. Non-guessing techniques never assume either truth or falsehood about any candidate or group of candidates. Evidence obtained by breaking this rule cannot help but be tainted by the assumption. None of our currently accepted basic methods force the solver to break this rule to apply the deduction.

As far as some of our advanced techniques go, by this definition...

NxN swordfish are non-guessing

Colors, multi-colors, etc. are non-guessing so long as no unwarranted assumption is made regarding any particular color representing true or false.

XY-Wings are non-guessing

Turbot Fish are non-guessing

Forcing chains, X-Cycles, XY-Cycles are non-guessing so long as the chain pattern is equally effective at making the reduction if the cells are true or false.

ALS XZ-Rule is non-guessing.

Grouping and/or Filleting augmentations to non-guessing rules are also non-guessing.

Uniqueness+1 and BUG+1 deductions are non-guessing. Plus more candidates deductions can possibly be tainted depend on the situation and how they are used.

Implication chains and networks deductions are tainted if they only apply when certain candidates have certain values.

Bifurcation is a guessing method.

Limited Bifurcation is a guessing method--no matter what limits you put on it.

Sherlock is a guessing method.

Backdoor Pairs is a guessing method.

Finally, tainted evidence is often forgiven so long as a non-guessing alternative is readily apparent. Thus, if you identify your naked pair reductions by noting that placing a naked pair candidate in one of the other cells in the group leads to a crash, rather than simply removing the naked pair candidates from all other cells in the group; almost no one is going to complain.

Nishio, as it is usually performed, is a guessing method. However Nishio could be accomplished by taking a solution pattern template built via symmetry and implication rules, and killing all patterns in cells that do not have the nishio digit as a candidate. It's not really a readily apparent alternative, however some may feel inclined to forgive its use for this and other reasons.