“They’re all a bit slow,” she said as we walked to the van. “Some of them can barely count.”

“Sweetheart, they are the finest minds in mathematics today; you should be happy that they’re coming to you for tutoring. It must have been a bit of a shock to the mathematics fraternity when you revealed that there were sixteen more odd numbers then even ones.”

“Seventeen,” she corrected me. “I thought of another one on the bus this morning. The odd-even disparity is the easy bit,” she explained. “The hard part is trying to explain that there actually is a highest number, a fact that tends to throw all work regarding infinite sets into a flat spin.”

Clearly, the seriously smart genes that Mycroft had inherited from his father had bypassed my mother and me but appeared in Tuesday. It was odd to think that Mycroft’s two sons were known collectively as “the Stupids”—and it wasn’t an ironic title either.

Tuesday groaned again when she saw we were driving home in the Acme Carpets van but agreed to get in when I pointed out that a long walk home was the only alternative. She scrunched down in her seat so as not to be spotted.

We didn’t go straight home. I’d spoken to Spike before leaving work, and he mentioned that he had some news about Mycroft’s haunting and agreed to meet me at Mum’s. When I arrived, she and Polly were in the kitchen bickering about something pointless, such as the average size of an orange, so I left Tuesday with them: Mother to burn her a cake and Polly to discuss advanced Nextian Geometry.

“Hiya,” I said to Spike, who’d been waiting in his car.

“Yo. Thought about what to do with Felix8?”

“Not yet. I’ll interview him again later this evening.”

“As you wish. I made a few inquiries on the other side. Remember my dead partner, Chesney? He said Mycroft’s spooking was what we call a Nonrecurring Informative Phantasm.”

“You have them categorized?”

“Sure. The A-list contains Pointless Screamer, Crisis Warner, Murder Avenger and Recurrent Dreary. From there it’s all downhill: poltergeists, faceless orbs, quasi-religious visions and phantom smells—more usually associated with recently departed pet Labradors.”

We walked up the garden path to Mycroft’s workshop.

“I get the picture. So what does it all mean?” I asked.

“It means that Mycroft had something he wanted to say before he died—but didn’t manage to. It was obviously important enough for him to be given a license to come back, if only for a few hours. Turn off your cell phone.”

I reached into my pocket and did as he asked.

“Radio waves scramble their energy field,” he explained. “Spooking’s dropped big-time since the cell-phone network kicked in. I’m amazed there are any ghosts left at all. Ready?”

“Ready.”