"Legacy? I wonder what that can be about?" mused Mike.

"Well, if it's a legacy then it must be old," said Ellie. "And if there's anybody who knows about old hidden puzzles and secrets, then it's Barquith."

As they left Jodrell Bank, heading to the Manchester Museum, a watcher from a nearby window muttered "Good-o. Well, you'll be back soon enough."

--

When Mike and Ellie arrived at the Museum, they saw a familiar face loitering in the foyer. "There's Mr Thornhill, our headmaster", whispered Mike.

"Good!" said Mr Thornhill, as he approached them. "I thought you'd end up here. It's important that we keep an eye on what our star pupils are up to. Now, if you'll excuse me, I have some other pupils to spy on!"

Mike and Ellie exchanged bemused glances and walked over to the main desk. The receptionist started telling them all about Barquith's latest obsession. "He's been busy studying prime numbers recently. Personally, I think maths is boring - too much long division for my liking - but he's always loved it and keeps trying to get me interested! Apparently, internet security relies on prime numbers - something about the fact that it's easy to multiply numbers together, but it's very hard to divide them. Honestly, I could have told him that... long division, uggh. He told me that every number can be factorised into prime numbers, but even the most powerful computers owned by GCHQ and the NSA might take years to do the factorisation. I've seen him factorise small numbers by hand for fun! Doesn't sound like fun to me. Still if these prime numbers keep my credit card details safe on the internet, then I guess maths has some uses!"

Mike and Ellie both laughed. "We like maths!" said Mike. "And codes!" added Ellie. "Is he in today? We've got something that we think he'll find very interesting."

A look of concern spread across the receptionist's face. "Actually, I haven't seen him for a few days. Last time he was in, he looked worried and mentioned that he thought he was in some kind of trouble. I didn't believe him at the time, but now I'm not so sure."

Ellie looked at Mike, both wondering where Barquith had got to.

"I've just remembered!" exclaimed the receptionist. "He said that if two code-obsessed kids came looking for him then I was to give them this." She reached under the desk, pulled out a sheet of paper, and gave it to them.

Alan Turing Cryptography Competition 2014 is organised by the The Department of Mathematics at The University of Manchester.
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