I happened to stumble upon something about this series by Asimov. Most of the stories seem to have been written in the 1970s. They sound interesting and involve fictional portraits of authors or personalities we have discussed elsewhere in other chambers and eyries of the Vault:
I've read through about three and a half volumes of the Black Widowers tales now. And one thing I've learned from reading them is that, left to their own devices, middle aged straight guys can be just as vituperative, catty and disputatious (let's avoid saying "bitchy," shall we?) as "the ladies who lunch" or a cabal of gay men.
While formulaic and thus somewhat repetitive, the stories are diverting little puzzles for readers either amused by or inured to the foibles and fetishes found among genre writers of the mid 20th century. The only ones that don't work for me are stories that Asimov set up as an excuse to ride one of his hobbyhorses. These include the fascination he had for mathematical factoids of the solar system, his characteristic disdain for anything hinting at the metaphysical or supernatural, and his detestation for feminists and feminism ("Middle Name" in The Casebook of the Black Widowers). Perhaps it was this element of self-indulgence in certain of these tales that led him to claim that writing them was one of his favorite activities. He wrote over sixty stories in this series and a few others were written by friends of his as a jesting homage.
I don't know what specific term is used for stories that are built around a genius detective solving a specific type of puzzle (sometimes, they read almost like "story problems" in math class). Examples I recall from earlier reading are Jacques Futrelle's "Thinking Machine" tales and the Encyclopedia Brown books which were popular when I was in middle school (early 1970s, US). Often, the main interest of the Black Widowers stories is seeing just how lurid or complicated the insults will get with which various members of this elite little circle accost one another in their badinage.
Each story has an "afterword" in which Asimov provides various bits of comment and backstory regarding the composition of each respective yarn. The now unacceptable mores of the era in which these were published is present in moments such as the one where Asimov fondly reminisces about "the beautiful Eleanor Sullivan," editor of the Ellery Queen Mystery Magazine, and how entertaining she supposedly found it when he would "chase her around and around the desk" when delivering one of his stories to her office. This kind of thing led me to wonder if some of Asimov's works have been the object of mass bookburnings by some irate present-day enthusiasts.
It's only fair to report that Asimov did caricature himself as an egotistical science author named Mortimer Stellar in the story "When No Man Pursueth." The stories are fun to read as a kind of deliberately elaborated version of the kind of banter that would have been heard at genre conventions back in the 1970s and 1980s. Five collections were published during the author's lifetime, and a sixth was issued in 2003 after his death.