Kari joined her. “What is it?”

“Remember how I thought the Atlantean numerical system used base eight?” Nina began, running a fingertip down one of the columns, careful not to smear the charcoal markings. “But that didn’t work for the Challenge of Mind, right? And the statues of the Nereids in the temple-according to Plato, there should have been one hundred, but you counted seventy-three?”

Kari nodded. “Have you found out why?”

“I’m not sure…” Nina looked down at the bullets on the ground. There was a pile of empty magazines next to them. She held one up. “Eddie! How many bullets does one of these hold?”

“UMP? Thirty rounds.”

“So there’s over a hundred bullets here, good…” She picked up one of the bullets. “Okay, let’s see…”

Kneeling, she moved closer to the nearest Indian woman, giving her what she hoped was a friendly, non-threatening look. The woman reacted with suspicion, but didn’t back away as Nina picked up a piece of charcoal and a blank scrap of bark. On it, she made a small mark-the symbol for a single unit. Then she held up the bullet, pointing to the mark and raising her eyebrows questioningly. “One, yes? One?”

The woman stared at her oddly for a moment, before suddenly smiling, saying something. “She says yes,” di Salvo told her.

“Great! Okay…” Nina reached back and picked up a handful of bullets, dropping them next to her knees, then lined up two of them below the parchment before making a second mark next to the first. “Two?”

The woman nodded again. Nina added another six bullets to the line, then made more marks. Eight little ticks in a line…

Another nod. Nina smiled, then took a ninth bullet, placed it by the first row, then added another tick to the line. “Nine?”

The woman shook her head. Nina wiped away the nine marks, then instead drew an inverted V and pointed back at the bullets. “Nine?”

A second shake of the head, this time accompanied by a somewhat exasperated expression and what sounded like a mocking comment to the other Indians. A few of them chuckled, as did di Salvo. “What did she say?” Nina asked.

“That she can’t believe you don’t even know how to count,” he replied, amused even through his weariness.

The woman took the charcoal from her hand and added a single mark to the left of the symbol, then pointed at the nine bullets. “So that’s nine?” Nina said thoughtfully.

“What have you found?” asked Kari.

“Starkman’s guy thought the circumflex symbol on its own represented nine,” said Nina, mind racing. “But it doesn’t-I started to realize it when I saw how they count. They don’t use their fingers-they use the gaps between them. Watch.” She moved one of the bullets away from the others, then tapped a finger between the thumb and forefinger of her other hand. “One.” The Indian woman stared at her, not sure what she was doing. Nina put a second bullet by the first, and tapped the skin between her thumb and forefinger again, then that between her forefinger and middle finger. “One, two?”

The woman nodded, smiling again. She held up both her hands, quickly using the little finger of each to count off the gaps between the fingers of the other until she reached eight.

Nina realized the significance of the shape her hands formed, the tips of her little fingers touching after she stopped counting. “The circumflex-it represents eight ‘full’ gaps. So nine is represented by one circumflex plus one, which means that…” She pointed at the tally, where a single dot was followed by a pair of circumflexes. “That’s seventeen-one plus eight plus eight. But look, they don’t represent sixteen with two circumflexes, but with eight single units plus one circumflex. It’s like they’re filling up the gaps between their fingers, and each time they’re full, the next number is however many full hands of eight they have, plus one.”

“It’s not a linear progression,” Kari said, understanding.

“No wonder we couldn’t work out the puzzle in the temple-we were using the wrong system! It’s like a weird hybrid of notational and positional systems!”

“English, Doc,” groaned Chase.

“Okay, okay… In our system, you add a new column every time you multiply by ten, right? Tens, hundreds, thousands-it’s a regular progression. But in their system, which also seems to be the Atlantean system, the new symbols that we saw in the puzzle room aren’t introduced along the same regular progression-instead, they fill in the gaps…” she held up her open fingers, “so to speak. If they were using standard base eight, the next symbol, the circumflex, the little hat-”

“Yeah, I know what a circumflex is, Doc,” Chase said testily.

“Sorry. It would represent eight in a normal base eight system. But it doesn’t-it stands for eight, but doesn’t appear until you get to eight plus one. And the symbol after that, the leaning ‘L’-in base eight that would be sixty-four. But because this is a cumulative rather than linear progression, where you don’t advance until you’ve filled up each of the gaps between your fingers-”

“It comes in after eight groups of eight, plus eight,” Kari continued, excitedly pointing out the relevant group of symbols on the tally.

“Right! And the first time it’s used is at eight groups of eight, plus eight… and then plus one. Or-”

“Seventy-three!” they both cried simultaneously.

“Like the number of statues?” Chase asked, frowning as though he now had a new pain inside his head to add to all his other aches.

“Yes! Of course! That’s why Plato said there were a hundred! It was a misinterpretation of the Atlantean numerical system over the centuries. In their system, it’s the equivalent of one hundred, when the third digit comes in-but it’s not decimal or base eight. It’s a completely unique system.”

“But Qobras won’t know that,” Kari pointed out. “Which means that when he converts the latitudinal figures from the map into modern figures, they won’t be accurate.”

Nina brought the map into her mind’s eye. “No, they’ll be way off! They thought that the circumflex on its own was nine, and a circumflex plus a tick was ten. But a circumflex plus a tick really equals nine. Their figures are wrong-they’re one off! They thought the Cape of Good Hope was at latitude fifteen south-it’s not, it’s at latitude fourteen! So they should have divided the thirty-five degrees difference by seven Atlantean units, not eight, which means one Atlantean unit is five degrees. Atlantis is seven units north of the Amazon, and seven times five is-”

Chase laughed. “Even I can manage that! Thirty-five degrees north.”

“Plus one degree to account for the Amazon delta’s latitude above the equator,” Kari added. “So Atlantis is at thirty-six degrees north-which is in the Gulf of Cádiz! You were right!”

“They’re hundreds of miles off course!” Nina exclaimed, unable to hold in her excitement. “We can find it first; we can still beat them!”

Castille finished treating the wounded Indian. “All that is well and good, but I have a suggestion-before we start congratulating ourselves, can we at least get out of the jungle?”

“The satphone’s in my rucksack, Hugo,” said Chase, sounding tired. “Chuck it over and I’ll call the cavalry.”

“Ai, merveilleux,” Castille complained as he found the pack. “Another helicopter.”

Nina looked up at the circle of Indians still watching her. “What are we going to do about the tribe? Never mind the temple, their homes have been trashed because of us. They’re going to need help.”

“I can take care of that,” said di Salvo. “As a representative of the Brazilian government, I can say that the tribe has been officially located and contacted, eh? That means they are now protected.”

“Not quite the contact we were hoping for,” Nina observed. “They killed Hamilton, remember?”