gurth wrote:To come now to your sentence "...I never minded to show a contradiction for the wrong candidate afterwards."

Sorry for my poor English, i wanted to say the opposite

I never

cared to prove the other candidate wrong on paper. When i find the solution directly when testing a candidate, i dont like the puzzle and i am happy to have done with it. But this happens very seldom. I suppose, it would be the case more often for very hard puzzles, but those i never try on paper.

But when someone asks for help for a puzzle and it would happen then, i always feel obliged to give a proof. I suppose the questioner would think, i am kidding, when i say "try this number and you will see, it solves". Its like posting the solution grid.

So we have 2 different situations. The one is to try to solve a puzzle "quick and dirty" (e.g. championships) and the other to solve it "clean and fit for publishing". I can follow your arguments, when you tried 2 numbers and it was solved, but my first thought then is "how lucky you were". With some bad luck you would have been stuck again with at least one of the 2 possibilities.