Several days earlier

"...I go all with the dividiness," Buffy said, kicking the big-horned, gnarly-toothed demon in the gut, "and get… um…"

The Doctor poked his head out from behind the complicated gadget he was constructing, taking the sonic out from his teeth. "X²…"

The gnarly-toothed demon roared and punched at Buffy. She ducked, then grabbed up a nearby metal trash can and slammed it over the demon's head. "Okay, okay… x² + 50x + 2 equals..."

Clawed hands wrapped around the can, as the demon wrestled Buffy for it.

The Doctor soniced his gizmo, which spluttered into life. "Equals?"

The demon, with a roar, crumpled the trash can and tossed it aside. Swiped at Buffy — who dodged both claws and can, then threw herself at the demon, giving it a great big shove. "249!"

An illuminated open door sprung up from the Doctor's machine.

The demon didn't catch itself in time, and gave another roar as it skittered right through the door. The Doctor darted forwards, yanking a wire from the gizmo. Doorway and monster vanished. "43."

Buffy blinked. "Huh?"

"Not 249," the Doctor explained, swiftly dissecting his gizmo and pocketing the pieces. "243."

Buffy sighed. "I'm never going to get this."

"Nah, it's easy!" The Doctor pocketed the last part of the gizmo, then took out a piece of chalk and wrote out all the steps on a nearby blank wall. "See? Carry the four, and… 243!" He rapped his knuckles against it. "Now, it's just a regular old giraffe."

"Giraffe?"

"Polynomial," the Doctor corrected. "Sorry, brain reached for the wrong word there. Regular old polynomial!" He rapped his knuckles, again. "Easy peasy!"

Buffy studied the math. She still didn't feel any better about her big test, tomorrow.

On the street beside them, a group of teenagers stopped a car blaring loud music at a red light.

The Doctor noticed Buffy's despair. "Oh, come now! It's not so bad!" He beamed. "Bit of positive thinking — and you'll be right as ninepence. Worked for my TARDIS driving test!"

"I thought you said you failed that," Buffy said. She crossed her arms. "Twice."

The Doctor scratched the back of his head. "Well… twice-ish."

Buffy shot him a look. Then sighed and traced her fingers along the mathematics on the wall. "It all makes sense, I guess. I just…" She grimaced. "I dunno if I could come up with that, myself."

"Course you could," said the Doctor. "It'll be second nature to you. Like riding a bike! Or staking a vampire!"

Buffy just kept staring at the numbers on the wall.

"Tell you what," the Doctor offered, shoving his hands into his pockets. "Take the exam, tomorrow. See how you do. And if you need a bit more help…" He tossed her a small key — which she caught. "...drop by the TARDIS and I'll find you another study-monster."

Buffy stared between him and the key. "You're sticking around?"

The Doctor shrugged — then grinned at her and winked.

Buffy grinned back, tucking the key into a pocket.

Then she said her goodbyes and headed off.

The moment she left, the Doctor raced out to the car that was still blaring music, in the middle of the street. The light was now green, but the car was still there.

But empty.

The Doctor spun around, and headed to the car behind it. Same thing. He ran to the car behind that one. Same thing!

"Everyone's just vanished," the Doctor said. "Poof! Gone. Except, if they'd actually just vanished in a puff of smoke, these cars would be moving. Unless…" He examined the brake pedals. Each was still held down, as if being pressed by an invisible foot. "Oh. Now that's interesting." He scratched his head, intrigued. "Yep. Buffy Summers — it seems I really will be sticking around."