Greetings, gentle patron!
If you are encountering difficulty making progress on my sixth 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.
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 with so many ænigmas, it is ever so much easier to proceed when one has as much contextual information as possible. In this case, from time to time, some black squares will contain numbers that exactly match the number of available adjacent white squares; this tells you precisely where the remaining lights around that black square must be placed. Pray do not hesitate to fill in such lights immediately, as soon as you discover them.

Analogously, you will sometimes discover that the quantity of lights already placed adjacent to a numbered black square exactly matches said square's number. Should this occur, I pray you shall immediately mark any remaining adjacent white squares with dots, indicating your confidence that no lights may occupy them.

It may seem that all of these additional markings on the grid (i.e., the lines representing the beams of the lights, and the dots representing squares known not to contain lights) are but useless noise, unnecessary steps that do not contribute to the solution (which, after all, consists entirely of the lights alone). I implore you to lend this impression no credence whatsoever. In actuality, your swift progress in solving the ænigma utterly depends on your disciplined application of all such notational devices. To attempt solution without their aid is akin to a sculptor attempting to create great works with his right hand tied securely behind his back: it may, in theory, be possible for him to succeed, but only at great cost, and with much reduced likelihood.

As alluded to above, progress toward the solution to this ænigma will come almost entirely in the form of small, incremental steps, often adding but one or two dots marking spaces where lights may not be placed. Do not endeavour to rush ahead, attempting to guess or otherwise ascertain the positions of several lights in one fell swoop. The whole of your solution will come as the sum of many steps; “patience” and “perseverence” must be your watchwords.

The great majority of the deductions on the path to your solution will be relatively straightforward. The difficulty will come in determining where on the grid each deduction is to be found. Seek out locations where your options are most restricted, where some light can only be placed in one of two locations. Quite often, there will be multiple such locations, but in at least one of them, a simple analysis of the cases will readily yield results.

In each such case analysis, use your intuition to guess which of the two possibilities is most likely. Then do something you might find rather surprising: concentrate your analysis on the other option, the one you concluded was less likely! If your intuition was correct (and you must trust that it quite likely was), then your analysis of the opposite choice will most probably yield a contradiction in very few steps indeed, thereby proving your intuition correct!
Wishing you the best of solving luck,

