Anyone notice you can solve this one only looking at the left-hand twin? I really love the twin puzzle idea, but they always wind up being far too easy....

Sure, always you can solve a twin looking to only one side, according to my theory. I talked about this in the forum, you may see the topic "Solving twins (separating sides). User created Dec 16 and 22" (2017) (topic date: Dec 24, 2017), calcudoku.org/forum/viewtopic.php?f=3&t=1007 , in the Section "Solving strategies and tips", and the previous topic "The essential info in a puzzle" (Oct 06, 2011), calcudoku.org/forum/viewtopic.php?f=3&t=77 .

A total of 83 and 123 puzzlers solved at that time (now probably there are many more solutions since the "User cretaed puzzles" have no expiration date) my two "User created puzzles" which in fact (with the previous authorization of Patrick to do the experiment in order to confirm my hypothesis) were the left (top in the book) and right (bottom in the book) sides of a 7x7 twin published in one of the Patrick Min books (nobody took notice of that in the days between Dec 16 and Dec 22, 2017 ).

It is probably possible to design a "cooperative twin" but not with the actual software (for the moment I have not found that case).

Best, clm.

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”.

I find a lot of them easy but not the twin no-op > a 6 grid......or in the bonus types with zeroes in the twin format......the larger twins do take some time but are enjoyable in that I do not have concentrate/think so hard.

Interesting and thoughtful reply as always, clm. I don't know enough about how the computer program generating the puzzles works to be able to either confirm or deny the point you are making, but I have absolutely no reason to doubt your analysis.

Regarding your statement that every puzzle with a unique solution can be solved using only analytical means, I'm not 100% sure how "only analytical means" should be defined. The easier puzzles can be solved from several starting points and involve mainly simple steps. The more difficult puzzles usually require a number of more complex steps. Sometimes this can require looking at overall totals (or products) for a row, column or quadrant, other times looking at the different possible solutions for a particular cage and how this might impact on other cages.

How many steps do you have to go down the line before a puzzle is regarded as being solved by 'trial and error', rather than by 'analytical means'? I don't think it's possible to specify an exact number of steps that moves the solution from one category to the other. I would argue that any limit on the number of steps is subjective and a matter of personal opinion.

Having said this, I think that it's possible (in theory at least) to determine the most 'elegant' solution to a puzzle i.e. the one that requires the least number of steps. And I would suggest that the step by step solutions that you have so kindly provided in the past to some of the more vexing puzzles represent very 'elegant' solutions to the puzzles in question, whereas other methods of solving the same puzzle that involve more 'trial and error' can also be regarded as analytical solutions, albeit less pleasing and well thought out.

I hope this doesn't come across as argumentative, but I find the subject interesting and just wanted to present my perspective on it.