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Billed as a "romantic crime thriller", Other People's Teeth is the tale of two interlocking relationships. One is conventional rom-com fare: the feisty Joss is dating the geeky Simon, who attempts to woo her with convoluted mathematical reasoning and games of chess. But the other relationship is between Joss and her boss Sol, and that partnership is anything but everyday. Because Sol is a hitman, Joss is his right-hand woman… and Sol isn't about to let the newcomer Simon get in the way.

For the first half-hour or so, I didn't entirely feel the menace inherent in this scenario. Dan Sareen intentionally plays Simon as a cool, dispassionate scientist – but perhaps he takes that detachment a little too far. Later on though, as the stakes get higher and Simon is ensnared in a relationship he can't leave, things grow genuinely tense. There is bluff and counter-bluff, and it's a credit to Sareen (who also wrote the script) that I wasn't at all sure how this nightmarish situation was going to end.

Even more sinister, and to me more thought-provoking, are the debates we witness between Joss and Sol – some of which take place in the very moments before a victim is killed. Each of the killers feels differently about what they do; Tom Claxton's creepily deranged Sol seems to be searching for some cosmic significance, while Becky Downing's Joss is more matter-of-fact yet somehow more humane. The tension between the two is disturbing, and often intriguing – and while there's a hint of sociopathy about both their characters, it manifests itself in unexpected and believably different ways.

The story is told through two interleaved series of scenes: one set runs forward in time, but the other runs backwards (so the first scene we see is actually the end of the story). Although this gimmick is clever, the interweaving is also confusing. It took me several minutes to realise that I had to pay attention to the dates of the voicemail messages played between scenes, and then a few more to figure out exactly what they were telling me. It would help a lot if Sareen and co-director Jess Williams could come up with a more obvious way of signalling the uneven passage of time.

Backwards-running stories – and I've watched a handful of them in the past – also tend to suffer from an underwhelming conclusion. I'm afraid I have to say I think Other People's Teeth is an example of this; when we finally get to see how the two killers met, it's a damp squib after the firecracker ending of the parallel storyline. Perhaps a shuffle of scenes would help, so that the forwards-running story delivers the finale, or perhaps there could be more of a mystery to be resolved by that fateful first meeting.

There is food for thought here though: questions about whether there are graduations of evil, whether one type of killing is worse than another, and about what it means to achieve equality within a fundamentally wicked career. The characters face meaningful dilemmas, and the blackouts between scenes often lead into surprises when the lights come back on. I hope the experience in Brighton will help shape this play as it travels on to Edinburgh.