CLEVELAND, OhioIn Ken Ludwig’s “Baskerville,” a cheekily clever adaptation of the Sherlock Holmes mystery “The Hound of the Baskervilles” by Sir Arthur Conan Doyle, the master sleuth considers the ramifications of a visitor who has just rung the doorbell of his famed, fictional residence at 221B Baker Street.

“Now is the dramatic moment of fate, Watson, when you hear a step upon the stair of someone walking into your life, and you know not whether for good or ill. What does Dr. Mortimer, man of science, ask of Sherlock Holmes, specialist in crime? And can he relieve the tedium of our mortal existence? Come in!”

Coincidentally, that’s the first question we should ask of any work of art. And here’s the inescapable conclusion: Directed with playfulness and vigor by Brendon Fox, “Baskerville” is a celebration of theater itself, a madcap homage to the artifice and inventiveness – and sheer unflagging energy – required to bring a play to life.

You Holmesian scholars can skip ahead, but for the rest, the story concerns the sudden death of Sir Charles Baskerville, heir to the Baskerville fortune. Dr. Mortimer believes his patient was scared to death by a monster dog, a hellish hound that superstitious locals claim had been feasting on Baskervilles for more than a century.

When Sir Henry, another member of the Baskerville bunch, comes to London by way of Texas to collect his inheritance, he takes up residence at lonely Baskerville Hall on the fog- shrouded moors of Devon. It’s up to Holmes and Watson to figure out who – or what – is offing members of the doomed clan before their new client becomes a chew toy.

“Baskerville” premiered at Arena Stage in Washington, D.C., in 2015 and feels like a natural follow-up to Ludwig’s “The Game’s Afoot,” another comic mystery romp. That one is set in Gillette Castle, the real-life home of American actor William Gillette, who earned his considerable fortune playing the un-stumpable detective onstage. (“Game” made its world premiere at the Allen Theatre in 2011.)

Like that earlier work, “Baskerville” offers no epiphanies and exists to entertain. In that way, the play is like Chinese food – it’s tasty and delightful going down, but don’t be surprised if you find yourself rummaging around in the fridge, a little hungry, hours later. Then again, who wants to live in a world without dim sum?

The fast-moving production is as fun as roller coasters were when you were 10, thanks to the show’s central conceit: Five actors play some 40 roles. The joy of “Baskerville” is seeing how they pull it off.

The challenge is even greater than it seems, because three actors are tasked with creating most of the characters. They are Brian Owen, Evan Alexander Smith and the great Nisi Sturgis, last seen in the 2012 Play House production of “In the Next Room, or the vibrator play.”

The remaining two – Rafael Untalan and Jacob James – anchor the show as Holmes and his stalwart sidekick Dr. Watson, respectively.

Everything rides on the ingenious quick changes, costumes engineered by Play House favorite Lex Liang (“The Crucible,” “The Little Foxes”) that morph from the voluminous skirts of a washer woman to the fancy, frilly duds of Sir Hugo, outfitted as a 17th-century Cavalier and the first Baskerville to fall to the great black beast.

Only vitamin B shots all around or truckloads of Red Bull can account for the speed with which the thespians race into and out of the wings, returning dressed in fresh duds, not a hair out of place – usually. (The occasional righting of a crooked hairpiece is part of the joke.) It’s no wonder the wardrobe team took a bow at the curtain call.

The hardworking cast also moves scenery – chairs and chaise lounges and cartoonish door and picture frames – on and off the stage.

Through it all, the well-oiled ensemble appears to be having a ball. Performers work up a literal sweat serving up one character after another, employing a cavalcade of burrs and brogues – as well as one well-utilized lisp – and a dizzying array of wigs and whiskers, courtesy of designers Mary Schilling-Martin and daughter Caitie.

One of the best reoccurring gags belongs to Sturgis as the Swedish wife of Barrymore (Owen), the hunchback butler of Baskerville Hall. As written, she is a collision of Inga from “Young Frankenstein” and the great Gilda Radner as Baba Wawa.

When Watson and Sir Henry discover a stranger skulking about the property, Mrs. Barrymore admits he is her “brudder,” a “conwict” named “Wictor.”

Watson: Pardon?

Mrs. Barrymore: A conwict. He vas incarserwated.

Sir Henry: What?

Mrs. Barrymore: He vas awwested, he vas in pwison!

Barrymore: He was in jail!

The show is as broad as Mrs. B’s accent, just as a thoroughly theatrical send-up should be. So pass the shrimp fried rice. Nothing wrong with carb-loading, especially in the dreary depths of winter.

“Baskerville: A Sherlock Holmes Mystery,” written by Ken Ludwig and directed by Brendon Fox, runs through Sunday, Feb. 12 at the Allen Theatre in downtown Cleveland’s Playhouse Square. Tickets are $25-$90. Go to clevelandplayhouse.com or call 216-241-6000. Approximate running time is two hours and 15 minutes, including one intermission.

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