Hi, Keith!Keith wrote:... we'll have to counsel you about using T&E on UR's*. Can there be a greater sin?
You're joking, right?
I maintain that it is logically defensible, and it is not "using" Uniqueness. The difference is simple.Keith wrote:So, we recognize a UR (and its result) and then we find another way to reason the same result.
This is logically defensible as not using Uniqueness?
-- To "use" Uniqueness is to adopt as axiomatic the statement "The solution to this puzzle is unique."
-- To recognize the "deadly pattern" and use it as a clue for finding a cell which might usefully serve as the root of a forcing chain is to say "If the solution to this puzzle is unique, then assuming that value 'x' lies in this cell will lead to a contradiction."
In the first case I must accept an axiom. In the second case I form an hypothesis, and test it against the rules of the game. The difference between the two procedures is as clear, I think, as the distinction between night and day.
Trust, but verify.
I've tried this route on quite a few puzzles. What I usually find is that the chain leading to a contradiction is very long.Keith wrote:Actually, it seems to me: Assume the deadly pattern, if it is a unique puzzle, you should pretty soon find a contradiction.
On the other hand, the chain leading to a contradiction when I start working from a "conjugate" cell is often quite short and direct. So experience tells me that the second approach is (usually) preferable. dcb