Howard smiled. “I’m trying,” he said.

Andy flicked his hair from his eyes and pushed his spectacles higher up his nose. “Okay, so now we can see which of the buildings are the right height and position to contain the sniper. And you can tell which floor he must be on to shoot at the required angle. Now, with only one sniper there are several positions which satisfy the position requirements.” He pointed to four positions on the three-dimensional map where buildings coincided with the circle. “But, if we increase the number of snipers, we restrict the number of options.”

Andy bent over the keyboard and began pressing keys quickly. The shapes disappeared from the screen and he added two more snipers, each linked to the target with a dotted line. “With three points to work with, the positions become more fixed, each has a spatial relationship with the others, and with the target. This time we don’t get a circle, we have a tetrahedron . . .” A three-dimensional four-sided shape appeared on the screen, like a knifepoint sticking into the ground. “Now it becomes much more difficult to fit this shape into the model of the city.” He called up the coloured blocks again. “See, all three points representing the snipers have to be in the correct position. There is only one solution.” He pointed to the three places where the sniper positions coincided with the buildings.

Howard drank his coffee. “How long did it take you to set this up?” he asked.

Andy beamed. “About three hours, but this model is really simplistic. A true working model will be much more complicated.”

“But possible?”

“Of course.”

“How long would it take?”

Andy shrugged. “The snipers and target model would take a few hours, but getting the measurements and angles is the hard part. I’d have to go out to the desert and I’d need to give the video a thorough analysis.”

“You haven’t seen it yet?”

“Of course not,” said Andy. “Bonnie wouldn’t dream of bringing FBI work home with her. She’d stay in the lab all night, but bring work home? Never.”

“I can arrange for you to see it at the lab,” said Howard.

“Okay, and I’ll have to go out to Arizona. I’ll need the best part of a day there.”

“That’s no problem,” said Howard. “You can come back with me, tomorrow morning. You can watch the video when you get back. And I already have a list of places where the President is going to be. We can use them to see if your system works. Can I ask you something, though? What do you get out of this? I mean, the FBI will cover expenses, and I guess we could come up with some consulting fees, but there’s still a lot of work involved.”