It’s been commissioned out of the BBC’s comedy department, but Ludwig falls into the same category of charming whodunits as Death In Paradise or Father Brown – both of which writer Mark Brotherhood cut his teeth on – which would normally be categorised as drama.

However, it has got a few comic elements, and crucially stars David Mitchell. Indeed, it’s impossible to imagine anyone but him in the lead role, which is testament to how much he occupies a certain sort of tweedy uptight character and makes the show instantly feel reassuringly familiar.

Here he plays John, a bookish loner who spends his days locked away from the world – just as he likes it – compiling crosswords under the pseudonym Ludwig, the certain logic of a puzzle so much easier to deal with than messy, noisy, unknowable humans.

But he’s forced to abandon that world when his identical twin, a respected DCI in Cambridge, mysteriously goes missing, fleeing from some imminent mortal threat. His wife Lucy (the always excellent but rather underused Anna Maxwell Martin) asks if John would pose as his brother James, slip into the police station and recover his notebook so she can figure out what happened to him.

And wouldn’t you know it… John immediately gets roped into a murder case that he solves with his detached rationality, while his sidekick DCI Russell Carter (Dipo Ola) looks slightly baffled by his partner’s newly odd behaviour.

This ‘murder of the week’ is dispensed with way too quickly for viewers at home to even hope to play along with, as instead the opening episode sets up the bigger arc of what might have happened to James, and establises just how much of a fish out of water John is.

He’s overwhelmed by the world - at least until he can put his mind to solving the riddle of a crime - but more pragmatically struggles with wearing contacts, driving a car and resisting the urge to fill his jacket pocket with pens for easy access, even if his brother would never do something so nerdy. All of which provide the hour with its quirky comedy moments.

Of course, it’s an outlandish premise, and one with more holes than a cheese grater. Not one of the top-flight coppers – except perhaps Sophie Willan’s character Holly – fully suspects anything is wrong… and the desperate threat to a hardened police detective doesn’t seem so imminent when John’s standing in for him. However, we are led to suspect that Chief Constable Ziegler is up to no good… not least because he’s played by Ralph Inerson (still Finchy from The Office to many), who always exudes nefariousness. 

Still, Mitchell makes it relatively easy to suspend disbelief, inhabiting the role of our fretful, socially awkward, but intelligent hero as comfortably as the sort of old jumper Ludwig would wear.

And despite the preposterous twins set-up, we’re in familiar territory with a socially misfit detective solving Richard Osman/Agatha Christie style crimes against the backdrop of a photogenic British city. It’s Monk meets Morse meets Midsomer Murders – and that’s just the ‘M’s – yet successfully walks the tightrope between not taking itself too seriously yet having enough drama to ensure the viewer remains invested. That’s one puzzle everyone involved has solved.

• Ludwig airs on BBC One at 9pm tonight, and the full series is available now on iPlayer. David Mitchell talks about the series here.