Greetings, gentle patron!
If you are encountering difficulty making progress on my third ænigma, perhaps you'll find relief in some or all of the following pedagogical aids.
First, I have collected a small assortment of advisory notes, or ‘tips’ as one might say, which are enumerated a bit below on this page.
Finally, if you remain perplexed or frustrated even after perusing that narrative, I have prepared further pages comprising hints on attacking the main ænigma itself. Those pages progress in stepwise fashion, each page revealing only a little more of the solution at a time. You may thus easily read just as far as you require to escape the cognitive quagmire of the moment, without the risk of seeing too much and spoiling what remains of your solving experience.
I trust that these resources will suffice to lift your mental ship off the shoals of perplexity and allow you happily to continue your journey down the river of clarity and deciperment, but if you find that they do not, I invite you to contact my associate, Pavel Curtis, directly for more individualized furtherance.
With my very best wishes for your imminent enlightenment,

As any person engaged in mathematical or scientific endeavours will agree, the choice of a good notation is of paramount importance: a wellchosen notation makes critical information instantly accessible and greatly improves both the ease of making inferences and the likelihood of those inferences being accurate.
In the current case, I strongly advise that you rigidly adopt two such notations: (a) really darken every square that you have concluded must be dark in the solution, and (b) make a small but distinct mark (such as an ‘X’) in every square that you know must be white in the solution. The example shewn on the ænigma paper illustrates just such a notation.

As I mentioned on the ænigma paper, the darkened squares are quite important. In particular, recall the rule stating that all darkened squares must form a single connected group; that rule will be the primary driver of your progress through the grid. Always be observant for darkened groups that are nearly surrounded by squares that are known to be white; a darkened group that is threatened, with only one square left as an ‘escape route’, represents a opportunity for solving progress: you know that such a square must not be white, so you may safely conclude that it should be darkened!
If you are constant in your diligence in applying this rule of inference, much of the ænigma will fall to your will, seemingly without effort.

Recall the final rule given on the ænigma paper, stating that there may not anywhere exist a 2×2 area that is all darkened. This rule comes actively into play much less frequently than the one discussed above, but it is none the less critical to your solving success.
Maintain a wary eye for situations in which you have concluded that three of the squares in a particular 2×2 area must be darkened. When such a situation arises, you may invoke this rule to immediately conclude that the fourth square in that area must be white!
Wishing you the best of solving luck,

