This is not the cover of the edition I read, but this is a great cover, so I'm going to cheat!
Nine Times Nine, originally published by Boucher under the name of H.H. Holmes, is the first book featuring the character of Sister Ursula, and while I have radio plays by Boucher, this is the first time I read a novel by him. The book certainly reads very pleasantly: while not much really happens, the story feels like it's always moving about, and there are even some minor hardboiled-esque segments where Duncan has fisticuffs with people. While those segments aren't really necessary puzzle plot-wise, I found the story as told at least pleasant enough, and it didn't feel like it had been padded too much, nor did it really ever drag.
Overall, I also did very much like the plot about the Temple of Light, the cult and of course the Wandering Jew Ahasver. Makes you wonder why someone who's been wandering the Earth for almost two thousand years would just resort to murder, you'd think they'd have created a better network of dealing with things if you've been around for so long already! I do wish the book had explored the cult in more detail, as the book ultimately focuses much more on the Harrigan family in general, and to a somewhat lesser extent Ahasver alone, rather than the whole organization around him. The other cult-related element is the person Swami Virasenanda whose attempt on killing Wolfe was foiled by Duncan the first night he visited, but you don't really hear much about how he worked as a religious fraudster, he's just used as the character who already tried to kill Wolfe once before.
The main problem of the book is certainly the locked room, which is probably also signalled by the fact the book is dedicated to John Dickson Carr. In fact, a whole chapter of the book is basically also dedicated to the infamous Locked Room Lecture of Carr, as at a certain point, the characters actually start quoting from the lecture in an attempt to solve the locked room murder of Wolfe Harrigan. The problem itself is technically not a true locked room by the way: why almost all windows and doors were indeed locked from the inside, there was one door that had been under observation by one single witness. So the situation only becomes a true locked room mystery if we choose to believe this character. I think Boucher did consider this point, and tried to sell to the reader we could absolutely believe this character regarding this point, but I do think it didn't work too well. The thing Boucher tries to pull off regarding the credibility of this witness testimony definitely has interesting elements, and I can also see it working in specific situations, but here it kinda falls flat, for ultimately, it's still basically just "let's believe the witness for the sake of the story". You either need to explore that specific character a lot more, or have a very specific kind of situation or world, where you can really sell the idea that witness would not lie regarding what they saw, for this to work, but in Nine Times Nine, the attempt to guarantee to the reader the witness told the truth, still feels like Boucher is just imploring you to believe him for the plot to work. It also kinda falls flat, for the same argument for some reason doesn't work for the actual culprit, whom is portrayed somewhat similarly to the witness, but for some reason, it doesn't hold for them? The two clues I refer to are the kind I actually really like, and they can work really well in specific settings (not explaining in more detail here as it would spoil the book), but here they just don't work the way the story pretends they are doing. There is also a kind of dying message. If you're better educated than me, it might have been very useful. It's somewhat Ellery Queen-esque clue, not just because it's a dying clue, but also the meaning behind it. Though one does wonder how trustworthy the dying message would be in practical terms, as to pull that off while a person is dying...But if this had not been a Anthony Boucher, but Berkeley book, the dying message would certainly have been fake and been used to manipulate Sheringham into arriving at a false conclusion!
The actual how behind the locked room is... alright? Practically speaking, it seems like a bit of a risky trick to pull off, especially with only one single attempt and also it having been impossible for the culprit to control all possible witnesses roaming around the house at the same time: if even one person had been standing at the wrong place at the wrong time, they'd have been found out. It's not my favorite type of trick to create a locked room, but it's alright, though what I actually liked better, was the simple set-up by Sister Ursula to guide the other characters (and the reader) at arriving at the same conclusion as she did. The simple questions she asks at the start of the denouement are so obvious, but they very firmly guide you to the right answer. Sister Ursula is also quite a fun character; though religious, she's not quite as religious as say Father Brown, with an almost cheeky, mischievous side to her.
Nine Times Nine supposedly ranks among Edward D. Hoch's favorite locked room mysteries. It comes nowhere close my absolute favorites, but it's an enjoyable read nonetheless. I do think it shows a lot of potential elements that could have been worked out even better, but as a mystery novel written by someone who obviously really looked up to Carr (and while not reflected as strongly here, Queen), Nine Times Nine is certainly a book I can safely recommend for a few hours of fun mystery.