Carcul wrote:Making r5c5=2 doesn't lead to any contradiction. In fact, from r5c5=2 a turbot fish emerges that imply r2c2=2. Am I missing something?
Making R5C5=2 will make the outlined loop (+) consist solely of conjugate pairs of 2, and a 5-sided strongly linked loop is impossible. That's the whole essence of the Broken Wings technique, I believe.
BTW, even considering r1c1=1 the puzzle have 5 solutions.
Hmm, OK, I'll investigate a bit. I'm just implementing Uniqueness Rectangles in my solver now, and as far as I could see, it managed to solve the rest if make R5C5<>2 and R1C1=1. I'll re-check, though.
Edit: Hmm, I just re-checked, and my solver *does* manage to solve it if I set R1C1=1 after having done the Broken Wing elimination. It's not impossible that I have an error in my program, though. It would certainly not be the first time. But things do look okay at first glance... I can try to scribble down a solution path if necessary.
(Oops, one thing just struck me: My solution *does* rely on Unique Rectangles, so perhaps the grid *does* have multiple solutions, but a happy accident makes the UR do a correct elimination... Will investigate further.)
Edit 2: Oh crap, that was exactly the situation. I disabled the UR test, and found several solutions by using trial and error. Oh well, R1C1=6 does, as gsf pointed out, lead to a unique solution. The point was nevertheless to demonstrate a Broken Wing which wasn't an X-Cycle, which I hope I did.
Regards,
Vidar-who-won't-take-lightly-on-hand-building-demo-puzzles-from-now-on