“Nothing in June or July,” I murmured out loud. My hand lifted. I pressed my fingers to the day that would always jump out at me in any calendar. June 21st. That was the day my mother had disappeared. Like the rest of the days in June, it was unmarked on Sloane’s calendar.

I scanned the remainder of the months, then moved on to the rest of the walls in our room. More calendars. More dates. Taking a step back, I took in the full scope of what Sloane had done. There were years’ worth of calendars on these walls, with the same dates marked on every one.

“Sloane?” I called toward the bathroom. The door was closed, but a moment later, I got a reply.

“I’m not naked!”

In Sloane-speak, that was as good as an invitation to come in. “Did you sleep at all last night?” I asked as I opened the door.

“Negative,” Sloane replied. She was wrapped in a towel and staring at the mirror. Her hair was wet. On the mirror’s surface she’d drawn a Fibonacci spiral. It covered her face in the reflection.

Sloane stared at herself through the spiral. “My mother was a dancer,” she said suddenly. “A showgirl. She was very beautiful.”

That was the first time I’d ever heard Sloane mention her mother. I knew, then, that she’d been awake all night for a reason beyond the papers on the walls.

“My biological father likes beautiful things.” Sloane turned to look at me. “Tory is aesthetically appealing, don’t you think? And the other girl with Aaron was very symmetrical.”

You’re wondering if Aaron takes after your father. You’re wondering if Tory is his secret, the way your mother was his father’s.

“Sloane—” I started to say, but she cut me off.

“It doesn’t matter,” Sloane said, in the tone of someone to whom it mattered very much. “January twelfth,” she said fiercely. “That’s what matters. Today’s the ninth. We have three days.”

“Three days?” I repeated.

Sloane nodded. “Until he kills again.”

“Tertium. Tertium. Tertium.” Sloane stood in the middle of our suite, gesturing to the paper-covered walls. “Three times three is nine.”

I need nine.

“And three times three times three,” Sloane continued, “is twenty-seven.”

Tertium. Tertium. Tertium. Three times three times three.

“Remember what I said yesterday about the dates and how I think they’re derived from the Fibonacci sequence?” Sloane said. “I spent all night going through the different possible methods of derivation. But this one”—she pointed to the first wall I’d investigated—“is the only version where, if you end the sequence twenty-seven dates in, you also end up with exactly three repetitions within the sequence.”

Three. Three times three times three.

“It was just a theory,” Sloane said. “But then I hacked the FBI’s server.”

“You what?”

“I did a search over the past fifteen years,” Sloane clarified helpfully. “For murders committed on January first.”

“You hacked the FBI?” I said incredulously.

“And Interpol,” Sloane replied brightly. “And you’ll never guess what I found.”

Security holes that the world’s most elite crime-solving agencies seriously need to patch?

“Eleven years ago there was a serial killer in upstate New York.” Sloane walked over to the next wall, years’ worth of calendars papering it from ceiling to floor. She knelt and pressed her fingers to one of the calendar pages.

“The first victim—a prostitute—turned up dead on August first of that year.” She moved her hand down the page. “Second victim on August ninth, third victim on August thirteenth.” She moved on to the next page. “September first, September fourteenth.” She bypassed October. “November second, November twenty-third.” She slowed as she brought her hand to rest on the date marked in December. “December third.”

She looked up at me, and I did the mental count. Eight, I thought. That’s eight.

I looked for the next date. January first.

“It’s the same pattern,” Sloane said. “Just with a different start date.” She turned to the last wall. There was a single piece of paper on it. The first thirteen numbers of the Fibonacci sequence.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233

“1/1,” Sloane said, “January first. In the first iteration I tried, the second date generated was 1/2. But that method limits you to dates in the first third of the month. Hardly efficient. Instead…” She drew a square around the second 1 and the 2 that followed it. “Voila. 1/12. Split in a different spot, that’s 11/2, so we add both of those dates to the list. Tack on the next digit in the sequence, and you’ve got 11/23. Once we’ve made all the dates we possibly can including the first integer in the sequence, we move on to the second. That gives us 1/2 and 1/23. And if you split 1/23 after the two instead of the one, that gives us 12/3. Then on to the third integer, 2/3. February only has twenty-eight days, so 2/35 is just filler. We go on to 3/5, then 5/8, 8/1, 8/13, 1/3, 3/2, 3/21, 2/1, 2/13, 1/3—you see how January third just repeated?”

My brain raced as I tried to keep up.

“If you end the sequence after it’s produced twenty-seven dates—three times three times three—you’ve generated exactly three repeated dates: January third, February third, and May eighth.”