Suggestions for a mystery with an ingenious plot

Hello everyone! I'm looking for a mystery which isn't centered around a crime, but rather a puzzle/series of puzzles/quest with an engaging plot.

This is my first foray into the genre; seemingly, I've managed to dodge almost all authors who fall into this wide genre! So, I'm really open to suggestions to look into with the main criteria being something to get me engaged with the storyline.

If something with a fascinating plot comes to mind, I'd really love to start off with that to whet my teeth on the genre!

Thanks everyone!

Most of the ones I can think have a crime somewhere as part of the puzzle but I think two Charlotte Armstrong books The Dream walker and The Gift Shop. Chrsitopher Brookmyre writes very funny crime novels with good puzzles. The Attack of the Unsinkable Rubber Ducks includes the solving of a number of "psychic" scams, and the Sacred Art of Stealing features a thief who is an illusionist.

Jeffrey Archer's Not a Penny More, Not a Penny Less might work for you in the ingenious-plot department. Four victims of a con man join forces and use their diverse professional skills to create a complex scheme for swindling him out of the money they lost.

Dorothy L. Sayers' Five Red Herrings does involve a crime, but the detection involves an insanely complex (but perfectly logical) analysis of railway schedules and could-X-have-been-at-Y-by-time-Z questions . . . and thus it *feels* like a puzzle story. Sayers The Nine Tailors does something similar with bell-ringing. Both are also excellent novels aside from the puzzle aspects.

John Dickson Carr's detective, Dr. Gideon Fell, frequently solved mysteries of the locked-room, "howdunnit?" sort, but I couldn't tell you whether (unlike Agatha Christie) he "played fair" with readers and avoided pulling rabbits out of hats.

Well, I have three suggestions. I hate to say it but you may be describing The DaVinci Code by Dan Brown. Despite its many weeks on best seller lists, it's not a great book, but it is fun and easy to read, and worth reading.

My other suggestion is to try an old Agatha Christie short story collection about her character Parker Pyne, Parker Pyne Investigates . He's a different kind of detective...he calls himself a "Heart Specialist", seeking to cure unhappiness. Definitely worth checking out.

You may also want to try Daughter of Time by Josephine Tey where a hospitalized detective spends his time researching the real mystery of the princes in the tower. Excellent.

Katherine Neville's The Eight might do the trick for you.

Aunt Dimity and the Next of Kin by Nancy Atherton is a puzzle mystery. The death is of natural causes. Not great lit, but fun.

If you don't mind dipping into the children's section, The Westing Game by Ellen Raskin is a fun puzzle mystery.

Somebody suggested Dorothy L. Sayers -- her Gaudy Night is fantastic and I wouldn't consider it to have a real crime in it.

The Daughter of Time by Josephine Tey is one of my favorite novels of all time in any genre, so I loudly second that one. Some of her other novels have more nebulous crimes embedded in layers and layers of mystery -- The Franchise Affair and Brat Farrar specifically come to mind.

The Quincunx by Charles Palliser might twisty enough for you ... it was a pretty fascinating read, the plot of which I couldn't do justice to ... however, per Wikipedia:

The book follows a theme of the number five - it traces five branches of one family over five generations, as they circle and maneuver around a fortune being determined in Chancery, and which of several wills (and one codicil) will be found valid. The book is divided into five parts, each taking the name of a branch of the family (although they don't necessarily focus on that branch of the family, but are still primarily told from the point of view of one character, John Huffam.) The family branches are The Huffams, The Mompessons, The Clothiers, The Palphramonds, and The Maliphants.

Each part is then divided into five books. And each book is then divided into five chapters. In general, in each book there are four chapters from first-person narrative of John Huffam, and then one chapter about other characters in a much more detached Dickensian tone, very similar to the way Esther Summerson's narratives are alternated with others stories in Bleak House.

In at least one case, this pattern is reversed, and there are four chapters about other characters, and only one about John Huffam.
As the chapters go by, quatrefoil roses from the family's arms are displayed at the top of each chapter, and at the beginning of each book, and you begin counting them down. At the end of the book there are five "quincunx" arrangements of five roses each, showing all five families' devices. This becomes an important visual clue later in the book, when a code of a sort must be broken using the heraldry as a guide.

Five parts of five books of five chapters each makes 125 chapters of this slowly unfurling story. The patterns continue, as at the very central chapter in the book, which is the 63rd one, the third story of the third book of the third part, there are five subsections, and what is revealed there, if the reader is perceptive, will make the plot clearer at the end of the book. (Palliser leaves it to the reader to figure out one key fact, which John Huffam only alludes to obliquely in the last few pages.)

At the end of each large "part" of 25 chapters, a partially revealed family tree is given, showing the parts that John Huffam has figured out, and some characters are shown on the tree who do not yet have a known connection to the family, but are displayed later.

Well, they do have crimes in them, but Donald Westlake's Dortmunder books are about committing the crimes, not solving them. Except while Dortmunder can come up with the most complex plots to steal anything, he has the WORST luck ever. He normally ends up having to go through six or seven plans to get the thing he's after and get away. I'd particularly try The Hot Rock, where Dortmunder has to keep stealing an emerald.

You may enjoy Headlong by Michael Frayn. The plot revolves around two academics figuring out whether a painting they have stumbled across is an authentic Renaissance piece or not. The storyline is gripping and it's quite an instructive book too!
I also find that Daphne DuMaurier has talent for creating mysterious and ambiguous atmospheres where things are not what they seem. Jamaica Inn and of course Rebecca are both excellent examples of that.

There are a couple of Amanda Cross Kate Fansler books and maybe a few of Lawrence Block's burglar series that do not feature murders although maybe there are crimes. Can't go wrong with either of these series in my opinion.

If you are looking for puzzles, you may be interested in Tales of the Black Widowers and More Tales of the Black Widowers, both by Isaac Asimov. Tho primarily a sci-fi writer, these are not sci-fi. Each chapter addresses a different puzzle or mystery presented to a group of men (book is copyright 1976) who meet monthly for dinner and during the course of the evening figure out the solution. I'm reading the 2nd book, and of the ten "mysteries" presented so far only a couple may or may not involve murder.

Another book which involves a crime but has very ingenious puzzle/plot is The Cuckoo Line Affair by Andrew Garve.