In front of the burgundy leather nailhead couch was an oak coffee table covered with magazines. Not covered exactly, Jessica realized, but tiled with magazines. Geometrically precise. Ten magazines, all opened, perfectly arranged, parallel and squared to each other. Two rows: five up, five below. Jessica looked at them a little more closely and discovered they were all crossword puzzle magazines. A pen lay on top of each, crossing the rectangle of off-white paper and black ink at a precise forty-five-degree angle. Ten magazines, ten pens.

“Wow,” Jessica began. “You must be a serious crossword puzzle fan.”

The woman waved a delicate, long-fingered hand. “Way beyond fan, I’m afraid,” she said. She crossed the space, eased herself onto the couch. Jessica noticed that the woman’s nails were done in the French manicure style. “Beyond addiction, even.”

“Beyond addiction?” Jessica asked. As a police officer she had encountered every kind of addict there was—drugs, booze, sex, gambling, porn, food. She didn’t know what the next level could be.

The woman nodded. “You see, the word ‘addiction’ hints at a cure.”

Jessica smiled. She stepped closer, and now saw that the magazines were published in what appeared to be ten different languages. All the puzzles were at some stage of completion.

Jessica was stunned. Who does this?

She glanced over at her partner, and noticed that Byrne seemed captivated by an elaborate display of brightly colored boxes on the bookshelves.

“I see you are intrigued with my collection,” the woman said to Byrne. “It is not very extensive, but it is well-balanced.”

“I feel like a kid in here.”

Laura Somerville smiled. “As George Bernard Shaw once said, ‘We don’t stop playing because we grow old, we grow old because we stop playing.’ ”

Men and games, Jessica thought. Her husband Vincent—a fellow PPD detective working out of Narcotics Field Unit North—was exactly the same way.

“What is this?” Byrne held up a beautiful white box. About six inches square, it appeared to be carved ivory. Whatever it was, it was old and delicate, probably a collectible.

The woman crossed the room, gently took the box from Byrne’s big hands—in a manner suggesting that it was both rare and expensive—and put it down on a sideboard.

“This is called a tangram puzzle,” she said.

Byrne nodded. “Never heard of it.”

“It is quite intriguing,” the woman said. “One of my passions.” She reached over, turned up a small latch on the box, and gently opened it to reveal seven small, intricately carved pieces of ivory, seven geometric shapes snugly tucked inside: five triangles of varying sizes, one square, one rhombus. Or maybe it was a parallelogram. Jessica hadn’t done all that well in geometry.

“It’s about three thousand years old,” she said. “The puzzle,” she added with a wink. “Not this edition.”

“It’s Chinese?” Byrne asked.

“The origin of the puzzle itself is in some doubt,” she continued. “It is most likely Chinese, although many Oriental games were really invented in Europe, then credited to the Orient in an attempt to make them seem more exotic.”

“It’s a jigsaw?”

“No, it’s what’s known as a rearrangement puzzle,” the woman said. “Rearrangement puzzles go back to Loculus Archimedes in the third century B.C. Or thereabouts.” She took one of the pieces from the box, held it up to the light. The ivory triangle shimmered small rainbows across the room. “This particular set was purchased at the Portobello Road market in London,” she added. “By an old suitor.”

Jessica saw a pastel glow rise in the woman’s cheeks. Old suitors sometimes did that to a woman’s memory.

“What’s the point of the exercise?” Byrne asked.

Jessica had to smile. Kevin Byrne was an endgame kind of guy. Jessica was all about the rules. It was one of the reasons they clicked as partners.

“The point of the puzzle is to solve it, young man,” Laura Somerville said. “To rearrange the pieces to match a diagram.”

Byrne grinned broadly. “Okay,” he said. “I’m game.”

The woman stared at Byrne for a moment, as if she had just been challenged. The word game seemed to bring her alive. “Are you?”

Byrne blushed a little. It was the Irish curse. Get cornered or challenged, you went red. Even the toughest of the tough.

Jessica wanted to get down to business, but Kevin Byrne was better at gauging when someone was ready to talk. This woman was not a threat. She was, instead, a cog in the wheel of an investigation. They had time. And it was about sixty-five degrees in here.

“I am,” Byrne said.

Laura Somerville reached into a drawer, removed a black velvet mat, placed it on the dining room table. She then carefully arranged the ivory tangram pieces on it. She handled them as if they were the bones of saints.

One square, five triangles, one parallelogram.

Laura then retrieved a tall book from a shelf. It was beautifully bound, thick. “This is a book of games,” she said. “It includes a history and collection of tangram. The author lives in Chester County.” She flipped through the three hundred or so pages. Page after page had a dozen silhouettes of geometrically shaped items on them—buildings, animals, people, flowers. She stopped at a page near the middle. “For instance, here is a page of problems created by Chien-Yun Chi in about 1855. It is a page of tools and household items.”

“All of these shapes are made from just these seven pieces?” Byrne asked.

“Yes.”

“Wow.” Byrne glanced at the diagram, studied it for a few moments.

She tapped a diagram at the bottom of the page. “This problem is a wedding drinking cup.”

Byrne glanced at Laura Somerville, then at the carved ivory pieces. “May I?”

“Oh, by all means,” she said.

“I’ll be careful,” Byrne said. For a big man, he was cautious, precise. Meticulous in his actions. When called for.

Byrne picked up the square and one of the large triangles. He stared at them closely, perhaps gauging their size and shape, their relationship to each other, his eyes darting from the diagram to the remaining pieces on the velvet.

He placed the big square on the velvet, the triangle to the right of it. He stared at the arrangement for a few seconds, then turned the triangle. He grasped two of the smaller triangles, held them over the emerging shape. He placed them on the table, moved them. He repeated this three or four times, his eyes roaming the geography of the puzzle.

A few minutes later, he was done. Jessica looked at both the diagram in the book and the arranged ivory pieces on the table. They were identical.

“Very impressive,” Laura said.

“Was this a tough one?” Byrne asked.

“Tough enough.”

Byrne beamed. He looked like a kid who had just hit a stand-up triple.

Jessica cleared her throat. “Right, well,” she said. “Way to go, partner.” It was time to get down to business. If they didn’t, Kevin Byrne would probably play with the puzzle all day.

Laura Somerville hesitated a moment, then gestured to the chairs in the living room. “Please. Sit down,” she said.

“This won’t take too long,” Jessica said. She took out her notebook, clicked a pen. “How long have you lived at this address?”

“Six years come October.”

“Do you live alone?”

“Yes,” she said.

“Do you know a young woman named Caitlin O’Riordan?”

The woman asked Jessica to repeat the name. She did. Laura Somerville seemed to think about it for a moment. “I’m sorry, the name doesn’t ring a bell.”

Jessica took out the photograph, handed it to the woman. “This is Caitlin,” she said. “Do you recognize her?”

The woman took the photograph from Jessica, slipped on a pair of rose-tinted bifocals, examined the picture in the bright sunlight streaming through the window overlooking Locust Street. “I’m sorry,” she said. “I do not.”