“Miss Scarlett with the candlestick in the ballroom!”

Perhaps to the uninitiated, answers to Bruce Adolphe’s mind-bending Piano Puzzlers sound something like those surprise reveals in the classic board game Clue—except that the range of references is so much vaster and zanier. “‘Puttin’ on the Ritz’ in the style of Beethoven!” would be an example. Or “‘Eleanor Rigby’ in the style of Brahms!” Or “‘Hava Nagila’ in the style of Bach!”

Popular tunes camouflaged within two-minute virtuoso miniatures in the style of a canonical composer, these are the conundrums the talented Mr. Adolphe writes for this country’s most popular classical music program, American Public Media’s 33-year-old “Performance Today.” An accomplished pianist as well, Adolphe presents a new Piano Puzzler each Wednesday, as one brave soul on the telephone teases out the references, sometimes in a flash, sometimes by tortuous trial and error. The complete segment runs about 10 minutes—just a blip, really, on a show that airs for two hours a day, five days a week—yet for many of the show’s 1.2 million listeners, it’s the jewel in the crown.

Not that the Piano Puzzlers exhaust the passions that drive Adolphe’s composing. In self-standing pieces of a very different kind, his mind is often on civil rights, social justice, and, most tellingly of all, the workings of the human brain. But the links he looks for are less literal than metaphorical.

“Whatever story I’m telling, I tell it through music,” Adolphe says. “I don’t want to pretend I’m doing something else.

“‘Puttin’ on the Ritz’ in the style of Beethoven!” or “‘Eleanor Rigby’ in the style of Brahms!”

“Once, after Yo-Yo Ma first played my piece Self Comes to Mind, which is inspired by neuroscience,” says Adolphe, “we got together onstage for a talk with Antonio Demasio, a neuroscientist I’m close to. And Antonio, who wrote me the text I had based the piece on, said something I’ll never forget: ‘No piece of music can approach the complexity of a single cell.’”

Like many figure-ground conundrums, Adolphe’s Piano Puzzlers have a way of tuning one’s antennae to subliminal mental processes for which one may not even have the words, yielding the reward of sheer delight. At present, the collection numbers better than 600 items. Fred Child, who has hosted “Performance Today” since 2000, reckons that the Complete Piano Puzzlers, played end to end, would run longer than Wagner’s Ring cycle.

Ah, to have been a fly on the wall at the 10th-anniversary dinner for the Piano Puzzlers in St. Paul, where “Performance Today” is recorded, or at a special concert at Schloss Leopoldskron for the Salzburg Global Institute, where Adolphe has lectured on several occasions. Here, in force, were fans who never missed a trick. “They weren’t just calling out a composer’s name but the exact piece I’m quoting,” Adolphe says. “‘Mack the Knife’ in the style of ‘Das Wandern,’ from Schubert’s Schöne Müllerin! ‘Danny Boy’ in the style of Debussy’s Arabesque No. 1! ‘I Won’t Dance’ in the style of Chopin’s Waltz No. 7, Op. 64, No. 2 in C-sharp minor!”

If the hidden tunes tend to the retro, there’s a reason for that. “They have to be able to stand on their own,” Adolphe says, “so they can withstand changes of harmony, mode, rhythmic complexity and still retain their profile and character. They have to be well crafted. That’s true of Rodgers or Arlen or Gershwin—lots of those guys in the Great American Songbook. It’s also true of the Beatles. For a lot of the pop songs today, it’s not. That doesn’t mean they don’t deserve to be popular. But take away a drum track or a chord progression, and there’s nothing left. A tune has to have great character and a strong profile to withstand my kind of compositional assault.”

Matthew Gurewitsch writes about classical music for Air Mail. He lives in Hawaii