But you are right, giulio, it is not well expressed, I missed part of the phrase " ... I think they all can be solved analytically (though this can be accelerated with minimum trial and error) ... ". Once you have obtained the numbers that compose all cages, for instance, and a big part of the puzzle filled, to "position" one of those numbers in a cage and see the global effect could be considered part of the analysis (this was already discussed, in some way it's like when you have to break 667 into its prime factors, you make attempts ... "it is not divisible by 2, 3, 5, 7, 11, ... ", until you reach the 23 and thus the 29), you could do it mentally, virtually, in abstract, but if you can gain time there is no sense when just writing the number with the pencil (or in the screen) helps (this is more or less what you are saying with ... "consider how permutations of different cages eliminate each other"). In other words, a puzzle would not be analytically doable if the only possibility to solve it is to be "lucky" among many many trials randomly performed and when you have spent a lot of hours. Perhaps we could define a "probability of solution" .

This is trial and error.

Hi, Patrick, giulio, picklepep, beaker, starling (the referred subject links in some way with the thread “Something I’ve always been curious about”) …

I have opened a new topic (in the section “Solving strategies and tips”) named “A 6x6: Is the analysis enough to solve a Calcudoku?” so perhaps we may continue there the debate on this subjects (the analysis and the “solver rating”) in order to “clear” the topic “what to do with the data” that sould mainly be oriented to the Patrick’s paper “On the Choice of Browser and Numerical Intelligence” (by the way the spectacular increase of puzzlers these recent days is clearly the result of the impact of the Patrick’s paper ).

A second reason to move the discussion is that this time I am including a detailed solution of a 6x6 that I think should be better located in that other section.