Too often translation is discussed in terms of loss. What hasn't come through? How is the translation inferior to the original? Multiples, refreshingly, does the opposite: it asks, instead, what is it that survives? And in particular, can something like "style", which we attach so closely to the specificities of linguistic activity, survive being wrenched out of a language entirely and remade in another? Novelist Adam Thirlwell devised an experiment to put these questions to the test. The outcome is this impossible, fascinating book.

The idea in brief: get a story translated several times in series (Russian to French, to English, to Dutch …) and as the distance from the original increases, watch what changes and what remains. To put extra strain on the original's integrity, Thirlwell invited novelists to do the translating. Many hadn't translated before. Some possessed – it transpired – only the ropiest understanding of the source language. And novelists are expected to have styles of their own (unlike us translators, who aren't allowed), so might struggle to avoid incorporating their particular stylistic distortions. How could an original survive?

Eventually the experiment would grow to comprise 12 stories, from Kharms to Kierkegaard, Vila-Matas to Miyazawa, Middleton to Kiš, each translated serially between four and six times (usually via English at alternate stages), featuring 18 languages and the translating talents/failings of 61 novelists. Each novelist was given only the (provisional) original they were to translate, but didn't see what had happened further upstream. The whole thing is big, preposterously ambitious and pleasingly silly. But meaningful, too, if you look closely enough. The devil, as every translator knows, is in the details.

Part of the pleasure of the translations being undertaken serially, rather than in parallel, comes from watching a little distortion or imprecision being compounded, or amplified, as the series progresses. A Lebanese story by Youssef Habchi El-Achkar features a setting rendered by Rawi Hage as a "coffee shop". Tristan Garcia's French translation calls it "le café" – not quite the same thing. In English, under Joe Dunthorne, this becomes a "cafe-bar". In Francesco Pacifico's Italian, next, "il bar". So we're now, apparently, in a bar. And it's in London. Which is absolutely not where we started.

Any translation is a new text built of a thousand tiny choices. But in Multiples a reader often won't know who's responsible for those choices. Who, after all, can read 18 languages? Being Anglophone, I can read Zadie Smith's English translation of a story by Giuseppe Pontiggia, and Tash Aw's English translation two steps further down – by which time the story is no longer set in Tuscany but in Guangzhou and has shifted to the present tense; but how can I know whether the relocation was Aw's, or from Ma Jian's in-between version in a Chinese I cannot read? A reader with Hebrew will find some things; a reader with access to Portuguese others.

Some writers are more anxious than others not to leave fingerprints. JM Coetzee and AS Byatt try for something close to what most professional translators aim to achieve: a story that's identical to the original, only with all the words changed; with no visible interference by one's own style. Personal style is a difficult habit to kick, however. In the note on her translation, Byatt refers to a moment that was just "too far from any sentence I myself would ever have written".

Other writers, of course, are more delinquent, deliberately perpetrating versions that don't aim to preserve or to replicate. Those who are more interested in deploying their own linguistic flashes and flourishes inevitably blur the picture. Lawrence Norfolk and his villanelle are quite seductive and very clever, but knowingly succumbing to the lure of infidelity leads to stories that, however interesting individually (or sometimes not), by disregarding essential links to their ancestry lose significance in this experiment. (Certain more intimidating originals absolutely insist on greater fidelity, naturally. "I'm not one to mess with Kierkegaard," says Jean-Christophe Valtat, reining himself back.)

Translation demands stylistic humility. And so the Spanish used in the translations by Javier Marías or Álvaro Enrigue isn't quite their own; it doesn't have their usual distinctive pulse or tone – their (in other words) style. Whereas the story by Florian Zeller is simply a story by Florian Zeller. Sometimes what's missing is just sympathy with the original, so the writer injects something new. Zeller's two-word sentence, "Enterré vivant." is revoiced by Wyatt Mason: "Buried alive, like a miner, in a mine, a deep, dark, dank, and – in all likelihood – Chilean mine."

There's no such thing as a perfect translation, and all these writers have produced translations of sorts. So is Multiples designed to fail? If it is, then it fails in multiple different ways – stories change, or resist, they shift in essential or merely cosmetic ways; some survive the process, others detach themselves entirely. By one measure, every translated story must be inadequate, yet each is still a distinct piece of writing that recently didn't exist. To anyone interested in translation – or perhaps more pertinently, in the effects of style – each failure is something new, something fascinating, that is gained.

• Daniel Hahn is the translator of The Investigation by Philippe Claudel.