What Ms. Sherry didn’t realize until much later was that Mr. Clough had a number of other ideas about her apartment that he didn’t share with her. It began when Mr. Klinsky threw in his two cents, a vague request that a poem he had written for and about his family be lodged in a wall somewhere, Ms. Sherry said, “put in a bottle and hidden away as if it were a time capsule.” (Ms. Sherry said that her husband is both dogged and romantic, a guy singularly focused on the welfare of children, not just his own. Mr. Klinsky runs Victory Schools, a charter school company that seeds schools in neighborhoods around the country, as well as an after-school program in East New York that his own children help out with regularly.)

Image PUZZLER Eric Clough, the designer, turned the high-end renovation into a Rube Goldberg-like contraption. Credit... Tony Cenicola/The New York Times

That got Mr. Clough, who is the sort of person who has a brainstorm on a daily basis, thinking about children and inspiration and how the latter strikes the former. “I’d just read something about Einstein being inspired by a compass he’d been given as a child,” he said. The Einstein story set Mr. Clough off, and he began to ponder ways to spark a child’s mind. “I was thinking that maybe there could be a game or a scavenger hunt embedded in the apartment  that was the beginning,” he said.

Before long, his firm, 212box, was knee-deep in code and cipher books, furnituremakers were devising secret compartments, and Mr. Clough’s former colleague, Heather Bensko, an architectural and graphic designer who had been his best friend at the Yale School of Architecture, found herself researching the lives of 40 historical figures, starting with Francis I of France and ending with Mrs. Post.

Ms. Bensko said she began writing chapters for a book, imagining scenes from the childhoods of those inspirational figures and trying to connect them. When that didn’t pan out as a narrative technique, she invented two best friends living in New York City who discover a mystery in an apartment and, in the course of unraveling the mystery, a sort of treasure hunt, they “meet” the historical figures.

All of that was tied into gizmos Mr. Clough, Ms. Bensko and others in their office hid in the apartment  without telling the clients  in a way that is almost too complicated to explain.

The renovation took a year and a half, and Mr. Clough, who acted as construction manager, brought it in for $300 a square foot, a rather conservative figure given the neighborhood and the scope of the project. Designing and producing the apartment’s hidden features, however, including its book and music, took four years, said Mr. Clough, who absorbed much of the cost in terms of his own billable hours, and relied on the generosity of more than 40 friends and artisans who became captivated by the project. He said he “begged, borrowed and stole” from them “in the collaborative process.”

“People were definitely not paid,” he said, “and we extend our thanks. It absorbed the minds of many people.”