Next day, crammed onto hard benches in a stuffy hut with nearly a hundred other girls, her head ached and somehow the big breakfast she’d consumed wasn’t settling. As she waited she took out her old schoolbook, glancing through the notes she’d made for her school cert exams, looking for nuggets of knowledge that might help her persuade them of her desirability as an RDF operator: how to calculate the surface area, arc length and areas of squares, polygons, circles and cones, the main theories of trigonometry and how vectors worked. The numbers seemed to swim before her eyes.

In the interview room was a table with a single chair on one side and, on the other, a man and a woman who barely acknowledged her presence save for a curt, ‘Miss Motts? Sit, please.’

She settled herself and waited.

‘So why do you want to be an RDF operator?’

‘Until the outbreak of war I was working at Bawdsey Manor.’ She saw their eyes widen, as she knew they would. It was a bold gambit and might backfire, but she’d decided to spin it anyway. Work at the Manor was always top secret, but Mark had told her that the name, along with that of Robert Watson-Watt, had become legendary.

‘I know almost nothing about what RDF is or does,’ she added quickly. ‘But I saw the interesting people involved in the work there, and that’s what inspired me to apply.’ She certainly had their attention. They shared a glance, and were now regarding her with the curiosity a biologist might give to a rare specimen.

‘Do you mind telling us a bit about what you were doing there, if it’s not confidential?’ the woman asked.

There was no point in lying; she’d soon be found out. ‘I was working in the kitchens.’

‘So you’re a cook?’

Kath’s heart sank, certain that her gambit had failed. ‘It was just an interim job, sir, after leaving school. But I have always been interested in science, especially physics and geometry.’

He gave her a withering look. ‘I admire your confidence, Miss Motts. Let’s have a little talk about what you actually do know.’

His first three questions were basic and she responded with ease. The fourth and fifth were harder, and she struggled before hazarding answers she felt by no means certain were correct. The final question foxed her completely.

‘Take your time,’ the woman said more kindly, pushing a notepad and pencil towards her. ‘Use this, if you like.’

She took a breath, drew a rough diagram and added the numbers. They simply didn’t make sense. Then she realised: it was a trick question. ‘I think you have me there,’ she said, turning towards the man with a slight tilt of her head and a single, oh-so-subtle flicker of her eyelashes. ‘Because unless Pythagoras was mistaken, the hypotenuse should have been three point four, not three point eight – which would mean that the vector is . . .’

He held up his hand to stop her.