It's an interesting question, and one that I have thought of a bit recently, because not only is Alzheimer's a family trait, but I recently suffered some minor brain damage in a bike accident, and have been doing some puzzles in part because there was little else to do, and in part to keep my brain ticking. Sudoku is pure logic, and as such it taxes a certain aspect of the brain, but it won't help if you have issues with word comprehension, vocabulary, and the like, and it won't help you to organize visual space much. You will also find, as you learn the tricks and acquire the ability to see the whole puzzle at once, that it becomes easier.
I think if you're doing this kind of thing as a mental exercise to keep your brain going, it's probably a good thing, but not by itself. One exercise my wife and I found more or less by accident and necessity (visual issues at first meant no reading allowed) is two-person crosswords. One person reads the clues and tells the other what spaces are left to fill, and the other does it blind. At least in my case, it's a good deal slower than doing it when one can see the whole puzzle, but it puts a pretty good load on your ability to recall words, remember lengths, etc. We have a daily paper whose puzzles and sudokus start very easy on Monday and become ferocious by Sunday, giving a good cross section. You can also get books of old NY Times crosswords, organized by day, with similar progressions.
I have read that visual stimulation is also important here, and that some of the less verbal computer games, such as Tetris, are useful. Finding a good Tetris that runs properly on modern computers may take a bit of searching. One that I used to do a lot, but that is very hard on keyboards as well as running too fast on modern machines is "Wordtris." A Tetris variant, it involves falling letters that one must form into words. It's a great challenge, and really keeps you on your toes. If you want a very simple visual game that will run on anything, find the original Windows 3.0 "samegame," which will run at least as far as Windows XP with no problem.
My mother, now 90, has had Alzheimer's for a long time, and has kept some of her faculties going doing word puzzles. Even now, though she barely knows what is happening around her and rarely remembers who I am, she can do wordsearch puzzles, and I think it's one of the things that has helped her, if not to avoid the disease, to be able to conceal it through not losing her vocabulary.
If you have not come across it, there's a website called "web Sudoku" that gives you an option of levels, and allows you to print out individual puzzles in a format that's very easy to work, one at a time. YOu can get hints on line as well if you need. It's a nice free service provided by a company whose actual specialty is printer ink. If you have a laser printer it's great!
