Re: 6x6 Twin Dec. 29 2019
paulv66 wrote:
clm wrote:
Sure, always you can solve a twin looking to only one side, according to my theory.
I hate to disagree, and I remember your experiment well.
But I think that the above statement is only true if you are prepared to allow the individual puzzles to have non unique solutions. While many twin puzzles will have unique solutions on both sides, not all of them will. But twinning them allows you to eliminate the non unique solutions.
First of all, thanks a lot for your “disagreement” and your attention and comments, this is a very interesting subject BTW a little bit discussed in the past.
Of course, it is possible to design a “cooperative twin”, to circumvent the affirmation, simply by preparing a left puzzle, let’s say an easy one, with two or three double uncertainties and then breaking those uncertainties with a right puzzle in order to obtain the unicity of the solution of the “combined” puzzle. But that would be a “prototype”, a simple “design”.
But in the, let's say, “real life”, in the weekly routine, that is, the 7x7’s on Mondays, the 5x5’s on Wednesdays and Thursdays and the 8x8's on Fridays, I have not found that situation and that's why I say “always”.
In the past (not actually, because now I try to minimize the time spent in solving the daily Calcudokus
), I used to solve only one side of the twins (it was more challenging to me) except when I was in a hurry in which case I used both sides simultaneously. And I always could do it. So, thinking in that, I planned the "experiment" using a 7x7 twin from a book, theorically more difficult that any 6x6 or 5x5.
I agree with the coolpapa’s comment
“… but they always wind up being far too easy … “. In general, this is the reality, they are easy, and in my opinion, this is because of the redundant information in the other side (I was referring to that in the mentioned post “The essential info in a puzzle”). Everybody is happy with the twins and that is probably because they are pleasant, relaxing and comfortable, that is, easy (this is very good, of course, for our "club", it’s like a soft drink, Spritz Aperol? or San Francisco?).
What I suspect is that the actual software “tests” (verifies) both sides for the unicity of the solution and not for a unique solution of the combined thing. I can understand this, it’s easier for the software, let’s suppose we have both sides with various different solutions, it would be complex to “match” a unique solution for the combined puzzle (clearly, the "ideal" situation is the "cooperative twin"). In these conditions, if the solution in each side is unique, then it can be solved separately from the colleague, which in fact becomes a simple friend but not an indispensable conjugated.
And, of course, it could be solved using only analytical means according to my “old theorem”: “
If a Calcudoku has a unique solution then it can be solved using only analytical means”.
The “philosophy” behind this “theorem” is as follows: If the solution is unique, only the main thread of the reasoning will we the correct one and will drive you to the appropiate conclusions and the final solution, while the many other lateral ways/branches will
always drive you to impossible situations, contradictions with the departure hypothesis or “data collision”.