Supposing you’re busily putzing along in your living room, humming a tune and thinking well of life, and then, uh-oh, you bump smack into a dead body. Well, there’s a problem. A merry one, too, in the hands of that momma of mysterious murderings, Agatha Christie. And leave it to Christie to transform a corpse into a rather amusing conundrum for Clarissa Hailsham-Brown, heroine of “The Spider’s Web,” which had a delicious opening Tuesday at Acadia Repertory Theatre in Somesville.

Wife of a diplomat and stepmother to his jittery daughter, Clarissa busies herself with household duties and a brain-twister game she calls “supposing.” In her spare thought time, she indulges her natural talent for crime by “supposing” all sorts of puzzler situations — and, much to her imagination’s delight, the one about finding a body comes true. Ergo, off she goes in a whirlwind of secret desk drawers, hidden alcoves and blunt objects, all of which reveal plots of forgery, blackmail, drug trafficking and murder.

Christie’s story line is as convoluted as a spider’s web, of course, and Acadia Rep weaves it into a jolly good evening of old-fashioned whodunitism. Director Ken Stack knows the murder mystery is this quaint theater’s strong suit, and he supportively has the actors take on the eccentricities and subtle humors of Christie’s quirky world.

Some could go even further, in fact. Doug Rainey as the inspector, and Joseph Lewis as the constable are flat, which is almost unthinkable in these plumb Christie roles. Rainey not only mumbles many of his lines, but he misses a knockout opportunity to let Christie’s words carry all their comic underpinnings.

More to the point of the Christie magic are Leslie Smith as Clarissa, Stephen McLaughlin as her charming guardian, Sir Rowland Delahaye, and Alan Gallant as the unwitting accomplice, Hugo Birch. These three — each in his or her own way — carry the show, keep it animated, intelligent and hopping largely because they are in the same sportive game of dare. Smith’s English accent is a thing of chance and she’s clearly not as young as the Clarissa of the script, but she’s at her best in this role.

Kathleen Lake, as the fearless and hardy gardener, Mildred Peake, comes on with a gusty bang, and Jonathan Mirin, as the suave Jeremy Warrender, has funny lines and a smile that just won’t quit (though it probably should).

Nkomo Morris as the disturbed child, Pippa, flails a bit too much and has a tiny voice that makes her quite sweet but incomprehensible. Ken Stack makes apt appearances as Clarissa’s stolid husband, and George Hamrah, as the slick Oliver Costello, is a crackerjack corpse.

Except for one ill-fitting suit on the inspector, costumes by Marilee Marchese are creamy and tweedy, a perfect complement to Stack’s brightly walled drawing-room set. Alan Gallant is the only actor misconstrued by makeup — including age lines and two big splotches of graying hair, which make him look as if he had a run-in with Mary Kay and lost.

If you’re looking for a good show for the family and especially for young sleuths, this is a sure thing. It has the right pace, the suspense and drollery you want from summer stock. Keep your eyes open: All the information you need to solve the mystery is onstage long before the characters tie it all together.

“Spider’s Web” will be presented 8:15 p.m. Tuesday-Sunday through Aug. 30, and 2 p.m. Aug. 31 at Acadia Repertory Theatre in Somesville. For tickets, call 244-7260.