Lobsang Ludd was sorted into Slytherin.

Jeremy Clockson was sorted into Ravenclaw.

Lobsang soon realised that stealing from people who shared his dormitory was far too easy to be worth it, compared with getting into other people's rooms at the orphanage without being caught. He needed the challenge of stealing from properly warded teachers' quarters, or at least from the other Houses' dormitories.

Jeremy, whose adoptive parents were computer geeks, missed the computer he was teaching himself to program on, and his dad's collection of antique proto-computers. It was frustrating that nothing electronic worked in Hogwarts. He kept a slide-rule with him as a fidget to play with when he got too stressed and needed something to calm him down.

Lobsang watched Jeremy give a clever answer to the riddle posed by the bronze eagle door-knocker that guarded the entrance to the Ravenclaw common room. And that didn't make sense, because obsessive, hardworking, literal-minded Jeremy wasn't the sort of person who could come up with a witty response like that. It was more the sort of comeback that Lobsang would have given. But then, he looked very like Jeremy, didn't he? Which meant that the person at the door had been Lobsang. He moved himself back in time a few minutes, and entered the room.

It was obvious which bed was Jeremy's. It was impeccably neat, as was the luggage trunk beside it, in which was arranged (Lobsang picked the lock to find out) a treasured collection of old-fashioned mechanical clocks and pre-electronic calculating devices.

He didn't have the heart to steal the slide-rule. But he left a few jinxes in the other beds for some of Jeremy's dorm-mates who he knew bullied the nerdy boy.

He hadn't expected, as he stepped back into the common room, to find Professor Level standing there. For one thing…

'Don't you teach Potions this period?' he asked. 'Third-year Slytherin and Gryffindor class?' He hoped he sounded convincingly like Jeremy, who seemed to have an impeccable memory for everyone's timetable.

'Indeed,' said Professor Level. 'And next period, I'm teaching second-year Hufflepuff and Ravenclaw Potions, and covering a third-year Care of Magical Creatures class for Professor Hagrid. Now, Mr Ludd, how do you think I'm going to manage that?'

'Isn't it obvious?' said Lobsang. 'You're using a time-turner. You have to avoid meeting yourself, or it can drive you mad.' He tried to sound matter-of-fact enough about it that Professor Level would assume this was what he did as well. In fact, he'd never needed the device to travel – and it was so limiting, always having to travel a precise number of hours back in time.

'Not exactly,' said Professor Level. 'Now, you must have realised there's a connection between you and Mr Clockson?'

'We're twins?' And Jeremy's adoptive parents hadn't felt able to take on two babies at once, so he'd been left behind in the orphanage…

'You're like me,' said Professor Level. 'People assumed I was twins, as well. And I grew up in an orphanage, like you. The difference is, I was never separated.'