Agatha Christie’s story of 10 strangers who are picked off one by one after being lured to an island mansion, And Then There Were None, has beaten Murder on the Orient Express and The Murder of Roger Ackroyd to be named the world’s favourite Christie novel.

The book, which Christie described as “so difficult to do that the idea had fascinated me”, and which the New York Times, on its publication in 1939, said was “utterly impossible and utterly fascinating … the most baffling mystery Agatha Christie has ever written”, triumphed in a public vote launched by the author’s estate to find her most popular novel. Set up to mark Christie’s 125th birthday on 15 September, the poll saw more than 15,000 people from around the world cast their votes, with And Then There Were None collecting 3,211. Murder on the Orient Express came in second, with The Murder of Roger Ackroyd third.

Mathew Prichard, Agatha Christie’s grandson and chairman of Agatha Christie Limited, said he wasn’t surprised by the result. “It’s probably the book my grandmother was proudest of,” he said. “It would have been a big surprise if it hadn’t won – it’s a very worthy winner.”

The novel, which is currently being adapted into a BBC One series starring Aidan Turner and Charles Dance, sees 10 strangers brought to an island mansion off the Devon coast by the mysterious UN Owen. Each of them has a dark secret, and as they eat dinner, a record begins to play, with a voice accusing them each of hiding something. Starting with reckless driver Tony Marston, who is killed by a dose of cyanide, they begin to die, the deaths reflecting the nursery rhyme “Ten Little Soldier Boys”. (“Ten little soldier boys went out to dine; One choked his little self then there were Nine.”)

“It you read it carefully, it rests on a knife edge,” said Prichard. “It’s very carefully and skilfully constructed, to get away, so to speak, with a plot as complicated as this, and to end up with a solution which you can actually see at the end that it works.”

According to the Christie estate, And Then There Were None has sold more than 100m copies worldwide, making it the bestselling crime novel of all time. The Christie titles competing for the crown of world’s favourite Agatha Christie novel were matched with celebrity backers, with David Suchet – who played Hercule Poirot in the long-running TV series – supporting The ABC Murders, calling it “one of Agatha Christie’s very best novels, [which] showcases the genius in her ability to produce so many novels about one detective, and yet come up with so many storylines.”

Thriller novelist Val McDermid had backed The Murder at the Vicarage, telling voters that “you could say in many ways that that one book is responsible for my entire career”.