Barquith handed the piece of paper back to Mortimer. "Why bother with such an easy code?" asked Barquith.

"We're so engrossed in our research on morphogenesis that people think we might not notice what's going on in the real world. An ordinary note could easily go unread, but not one in code."

"Morphogenesis?" said Barquith, his eyes lighting up. "Doesn't that refer to how biological organisms develop their distinctive shapes? Alan Turing developed a mathematical theory of morphogenesis to help understand how patterns form in nature"

"We've done some of that at school!" said Mike. "Like how Fibonacci numbers appear on pine cones and the golden ratio describes the shape of a snail's shell." "Or how snowflakes are examples of complicated shapes called fractals," said Ellie.

Cuddeny smiled. "Yes, and Turing's theory of morphogenesis is a similar idea. You start with some fairly simple mathematical equations, but when you solve them you get very complicated and intricate solutions. These solutions tell you how different patterns can form in nature: stripes on tigers, spots on leopards, that kind of thing. Turing worked out the mathematics of this back in the 1950s when he worked at the University of Manchester."

"And the government set up the Garamond Institue in the 1950s to exploit this idea," blurted out Izzy. "Professor Sir Henry Garamond was the first Director, and when he died his nephew Dr Charles Garamond took over."

"Dr Charles Garamond who was recently found dead, killed by Old Schuck, a ghostly hound?" queried Barquith. He looked at Cuddeny. "And now you're the new Director. Why did you come to see me?"

"I was wondering if you'd be able to spend some time at the Institute," said Cuddeny, "to find out who is behind the death of Dr Garamond. The family want to make sure that justice is served."

Barquith's eyes briefly narrowed in thought. "I'm afraid I'm far too busy to go there myself," he said. "But maybe Mike and Ellie here would be willing to help out. In fact, I'm sure that their parents will be happy for them to go camping on the moors for a few days and do some detective work. They can report their findings to me." Cuddeny considered this briefly then reluctantly nodded. "Now then, perhaps you'd let me get back to work," said Barquith, as he directed Cuddeny and Mortimer out of his office.

Once Cuddeny and Mortimer had left, Barquith turned to Mike and Ellie. "Perhaps you should follow those two, see where they're going", he said.

"Quick, get the bikes!" said Ellie to Mike, as she saw Cuddeny and Mortimer get into a taxi. "The taxi's number is 1729: keep an eye on it!" she shouted.

"Nothing special about that number!" said Mike, as they mounted their bikes and sped off to follow the taxi. They pedalled hard to keep up with the taxi as it dodged its way through the busy traffic. Finally, they caught up with it at Manchester Piccadilly Railway Station, just in time to see Cuddeny and Mortimer disappear into the rush-hour crowds.

"Lost them! We'll never find them in that crowd," said Ellie, as the now-empty taxi turned around and drove back towards them. "Come on, let's go home and start planning our camping trip instead."

Just as they were about to set off, the taxi left the taxi rank. As it passed Mike and Ellie, the taxi slowed and they saw that the driver's face was obscured by a thick black beard. The driver tossed a piece of paper out of the window and it landed at Ellie's feet. Ellie reached down and picked it up. "Mike," she said, "I think the game is afoot."

Alan Turing Cryptography Competition 2018 is organised by the The Department of Mathematics at The University of Manchester.
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