“I’m sorry,” said Kate. “It’s the only thing I can think of.”

At this suggestion everyone grew quiet, looking at one another with unpleasant feelings of suspicion.

“Well, there’s no point in putting it off,” Kate said. “If I’m right, we can figure this out pretty quickly. Let’s tell each other our birthdays.”

Everybody but Constance gave their birth dates at once — not a Gemini among them. But Constance refused. “This is nonsense. Even if I were a Gemini, which I’m not, we don’t know for sure that’s what the message means.”

“If you’re not a Gemini,” Sticky said, “why don’t you prove it?”

“You prove it yourself,” Constance snapped. “How do we know you didn’t lie? Can you prove when you were born, Mr. Capricorn?”

“Uh . . . ,” Sticky began, for of course he could not.

Constance turned to Kate. “What about you, Miss Taurus? Can you prove that you’re for us?”

Kate hesitated, trying to think of an indignant response that rhymed. Unfortunately, nothing seemed to rhyme with “Constance.”

“Can anybody here prove it?” Constance challenged.

“She’s right,” Reynie said, with a feeling of great relief. “There’s no way to prove it.” (Even in the dim moonlight he noted Constance’s look of gratitude — she’d been very worried about being considered a traitor.) “That’s actually good news,” Reynie went on, “because I’m convinced Mr. Benedict wouldn’t send a message that made us turn against one another — not if there wasn’t some way of proving the truth. The message must mean something else.”

“You keep forgetting,” Sticky said. “Mr. Benedict is here on the island. He’s not sending us any messages. He can’t be both places at once.”

“That’s it!” Reynie cried. The others shushed him.

“That’s it,” he repeated, this time in an excited whisper. “Both places at once! Sticky, what’s the sign for a Gemini?”

“Sign of the twin,” Sticky said offhandedly. His eyes widened. “Wait a minute!”

“That’s right,” said Reynie. “I think Mr. Benedict has a long lost brother.”

As is always the case with a society, some arguing remained to be done. Kate wanted to know why Mr. Benedict hadn’t told them he had a twin on the island, to which Reynie replied that he probably hadn’t known himself. But if he hadn’t known it then, Kate persisted, how did he know it now?

“The looking glass,” Reynie said with a grin. “Remember? ‘When looking in my looking glass I spied a trusted face.’ Mr. Benedict wasn’t referring to his mirror — he meant his telescope! They just set them up today, remember?”

“So he saw Mr. Curtain for the first time today,” said Sticky, “when looking through his telescope.”

“I’ll bet it was quite a shock,” Reynie said.

“But how could Mr. Benedict not know he had a twin?” Kate asked. “They were born together.”

“They must have been separated as babies,” Reynie said. “Mr. Benedict told me he was an orphan. When his parents died, he was sent here from Holland to live with his aunt. Mr. Curtain must have been sent somewhere else.”

“But they’re both geniuses, and they’ve always been interested in the same things,” Kate said, her imagination catching on, “and so at last they’ve been drawn together!”

“Wow,” said Sticky.

“Uh-huh. I’m sleepy,” said Constance, who chose not to be impressed.

Reynie ignored her. “It’s strange news but good news. At least now we know we haven’t been tricked. Sticky, better send them a message that says we understand.”

Sticky did so, and at once the light in the woods began flashing a response. Sticky watched closely, relating the words as they came: Good job. Good night. Good lu . . .

“They stopped signaling,” Sticky whispered, frowning. In a moment he saw the reason. “Executives! A pair of them have gone out onto the plaza. They’re just standing around talking. Now they’re sitting on a bench. Looks like they’re going to stay awhile.”

“The message was almost finished, anyway,” Kate said with a terrific yawn, “and frankly, I’m toasted. Can’t we call it a night?”

Reynie and Sticky agreed, but Constance was incredulous. “How can we call it a night? We don’t even know what they were going to say!”

Kate laughed. “Good grief, Constance! Are you joking?”

Constance was indignant. “Are you? It couldn’t possibly have been ‘good grief’! The second word started with ‘lu.’”

Startled, Kate opened her mouth to reply, but Reynie cut her off. “It’s a good point, Constance. In fact I’m pretty sure they were going to say ‘Good luck.’ Don’t you think?”

Constance seemed skeptical about this. After all, she said, they couldn’t be sure that’s what the word was going to be. But as she was sleepier than any of them — she’d been rubbing her eyes for an hour — she consented to adjourn the meeting.

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