Page 32 of The Final Vow

Bradshaw leaned forward and began numbering the squares. She started in the top left with Cumbria then worked her way down to Kent in the bottom right. She missed off Scotland completely. Cumbria was square number two – the lowest number you could throw with a pair of twenty-sided dice – and Kent was forty, the highest number you could throw. Whenshe’d finished, every inch of mainland England and Wales was covered by one of the thirty-nine squares.

Poe saw where Bradshaw was going.

So did Flynn. ‘You haven’t numbered Scotland, Tilly,’ she said. ‘Why?’

‘So far, his victims have all lived in squares two to forty,’ Bradshaw said. ‘He’s ignoring Scotland. It might be as Poe suggested – that he’s zeroing his rifle up there – or it might be for reasons we don’t yet understand.’

‘Gretna Green’s in Scotland, though.’

‘That’s only because England’s border with Scotland isn’t straight. It has a forty-five degree slope. When you put the two northern counties into squares, you also catch part of southern Scotland. If you look, you’ll see that some of Dumfries and Galloway is in the same square as Cumbria.’

‘Which includes Gretna Green,’ Poe said.

‘Yes.’

Bradshaw chewed her lip. ‘The datadoessupport him dividing up England and Wales this way, but this is a hypothesis. A tentative explanation for how he is choosing his locations.’

‘Explain the data, Tilly,’ Poe said. He knew Bradshaw well enough to know she didn’t guess. Everything she said was backed up by statistics.

‘The range of two icosahedrons is two to forty. That’s why I’ve sectioned England and Wales this way. Are you following so far?’

Poe and Flynn nodded. Mathers said, ‘Yes.’

‘And, as we’ve established, there are four hundred possible combinations when two icosahedrons are thrown.’

Again, they nodded.

‘But not all combinations are equal when it comes to probability. There’s a one in twenty chance of twenty-one being thrown, but only a one in four hundred chance of two or forty.’

‘The double one or the double twenty,’ Poe said.

‘That’s right,’ Bradshaw said. ‘The highest probability numbers are the middle range, the least probable are the outer range.’ She opened a small box on her laptop and typed in some commands. ‘Now, watch what happens when I populate the squares with the victim’s locations.’

Like a plague of chickenpox, red dots began popping up. Eighteen of them, one for each life the sniper had taken. Poe immediately saw what she meant – the highest concentration of murder victims was bunched around squares thirteen to twenty-nine. The mid-range numbers. The numbers that were statistically most likely to be thrown. On Bradshaw’s map that was North Wales and London and everywhere in between. Poe counted twelve victims. More than half. Jools Arreghini was in square twenty-seven. Five of the victimswereoutside of the main bunch, but within squares nine to thirty-four.

And then there was Naomi Etherington, the Gretna Green victim. She was the outlier Bradshaw had mentioned. Gretna Green was in grid number two. A double one. Snake eyes. And the odds of snake eyes being thrown were one in four hundred. No wonder Bradshaw had waited to voice her theory.

‘This is it,’ Mathers said, nodding. ‘Tilly’s right: this is how the bastard’s choosing who to shoot. He’s picking a square on a map based on the throw of fucking dice.’

‘And if it lands in a square he’s already killed in, he’ll rethrow until he hits a fresh one,’ Flynn said.

‘No wonder my boffins couldn’t find his victim type. He doesn’t have one.’

Flynn nodded. ‘Then, as he won’t want to leave anything to chance, he’ll just choose whatever location he thinks works best for that particular square.’

‘What do you think, Poe?’ Mathers asked.

‘You’re OK with the Gretna Green outlier, Tilly? That’s a one in four hundred roll of the dice.’

‘It’s probability, Poe. People win the lottery every week despite the ludicrous odds against it. A two being thrown is not unexpected. If the sample size were ten thousand, it would even out.’

‘Now we just need to find out who sells these . . . what did you call them, Tilly?’ Mathers said.

‘Icosahedrons?’

‘Yes, the twenty-sided dice.’

‘You can get them anywhere, Commander Mathers. Sometimes they’re part of a set of mixed dice, but they can be bought individually.’