I don’t really have a succinct answer, but I think that “solve-it-yourself mystery”, as said by James above, leads to some good search results.
It seems that Alfred Hitchcock also wrote some: “Alfred Hitchcock’s Solve-Them-Yourself Mysteries”.
I just wanted to say thanks for bringing this up, because I enjoy that type of story from time to time and I’m looking forward to reading more of it.
I think the genre was unfortunately never so popular as to get a widely recognized, definitive short name of its own. Actually, I recently asked myself how it’s called in German, because I fondly remembered reading some nice examples, and wanted to find more. I’ve seen them described as “Ratekrimi” (could be translated as “guessing mystery”) or “Rätselkrimi” (“puzzle mystery”) or “Kurzkrimi zum Mitraten” (“short mystery for guessing along”).
H.P. Karr, who wrote hundreds of very short versions of such mysteries (in German) for newspaper syndication, says on his website that the concept derives from the English format “Catch the Criminal”, where the story was combined with a small illustration which provided a further clue. I found one episode of the series online in an Irish magazine.
Karr also notes Lawrence Treat (“Crime and Puzzlement”) and John Sladek (“The Book of Clues”) as American examples.
Since the newspaper-style mysteries are very short, they provide a nice diversion, which is of course fine, and which is all they aim for. But in such a brief format, there is not much room for descriptions, red herrings, characterization and so on. I’d like to see slightly longer variants of the genre. The Encyclopedia Brown stories and the Hitchcock ones seem to go more in that direction (even though they are for young readers).