How did Jack Mooney solve the Marston murder case in Death in Paradise? Episode one explained

• Death in Paradise reveals full list of series seven guest stars – with actors from Car Share, Poldark, Game of Thrones and Doctor Who
• Meet the cast of Death in Paradise: Ardal O’Hanlon stars as Jack Mooney
• Who plays Siobhan Mooney in Death in Paradise? All you need to know about Ardal O'Hanlon's on-screen daughter

It was a fiendishly complicated case with an excellent cover-up. So how did Mooney work it out, based on a bottle of nail varnish and a hotel floor plan?

Why did it look like a suicide?

At first glance, this looked like an open and shut case of suicide. On the day of her wedding, Diane Smith (Elizabeth Berrington) was disturbed by a tabloid story about her past: "Secret Shame of Hotel Billionaire's Bride: hotelier's wife-to-be abandoned baby on church doorstep." She was in her room in the hotel, while her fiancé Philip Marston (Denis Lawson) and his daughter Karen Marston were downstairs welcoming 130 guests to the wedding.

Suddenly Philip received a text from Diane, saying "I can't do this any more." He raced up the stairs and tried to get into the room, but it was locked! A voice cried out from inside: "I can't, I'm sorry" – and then, seconds later, Diane plunged from a balcony. Outside, the guests watched in horror as her body hit the ground.

Mooney was convinced this was a murder, not a suicide – but the puzzle was this: how could Diane have been murdered if she was alone in a locked room? There was nobody in the room when Philip forced the door and burst in.

How was Diane murdered?

Here's what Mooney worked out:

In room 317, Diane had just begun painting her nails when she heard a knock at the door, so she went to open it without screwing the lid back on the bottle – thinking that she'd be back any second. (His first clue!)

The person at the door was her new stepdaughter Pearl Marston, who hated her. Diane was trying to get Pearl to do some work instead of living the life of luxury at her dad's expense, and a couple of weeks beforehand Diane had even been forced to call the police after Pearl turned up outside her door to harass her. In fact, it was Pearl who hired a PI to dig up dirt and leak the story to a "carefully chosen tabloid" – providing a motive for her apparent suicide.

Pearl told Diane that Stephen Marston needed to see her urgently in the room directly above hers – room 417. Diane rushed upstairs.

As soon as she was gone, Pearl slipped into the room, chained the door, and sent a text from Diane's phone saying "I can't do this any more." When Philip came rushing up the stairs she imitated Diane's voice and called out "I can't, I'm sorry," and then she hid in the bathroom until her father managed to force the door open.

Once he was out on the balcony she rushed back in, having apparently heard the commotion from her own bathroom just across the hallway.

Meanwhile, in room 417, Stephen – who had been in charge of room allocation – was preparing to kill Diane. As head of HR at the Marston Group she knew about a sexual harassment charge he was facing, so he wanted her out of the way. He manoeuvred her onto the balcony and, as Pearl called out from the room below, pushed her to her death.

None of the guests saw that Diane actually fell from the fourth floor balcony (not the third), because at that very moment Karen Marston was giving a speech and they were all facing in the opposite direction. Karen had been enraged when Diane refused to sign a pre-nuptial agreement that would have protected the family wealth.

"The killer was never in the room and neither was the victim," Mooney explained. But the Marston siblings had created an illusion to fool their father into believing it was a suicide.

All it took in the end to solve the case was a bottle of nail varnish, a hotel room plan and three strong motives for murder...

Death in Paradise continues on Thursday 11th January at 9pm on BBC1