Omake Week 2015, Day 6: Yukari is fun as heck to write about, but I'm still surprised that I was able to come up with more than one example of math-based humor...

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Yukari Yakumo stepped out onto the veranda and gave a yawn and a stretch, feeling the joints pop in her arms and shoulders. Sometimes, she thought to herself, a youkai just felt her age. Though, she noted, she thought she was doing rather well given that that age was several millennia.

She had overslept this evening, something made possible because she'd given her shikigami Ran a long list of chores to accomplish that would take her all over Gensokyo. By Yukari's estimation, Ran would just then be about halfway up Youkai Mountain dealing with a tengu-kappa boundary dispute, rather than in Yukari's bedroom pretending to be an alarm clock.

It was, she had to admit, a lovely evening. No clouds obscured the star-strewn sky, and the moon was a crimson sliver against the chartreuse background. Idly, she considered slightly tuning the barrier that kept the Yakumo residence isolated from random wanderers to adjust the colors, then decided that the effort would probably not be worth it. And she was expecting Eirin Yagokoro to drop by in the early morning, and she was interested in how the transplanted Lunarian would find her way past the current setting.

Thus, Yukari decided, she would simply relax on the veranda with a cup of tea to start her evening. Of course, one problem with Ran being absent was that tea was not going to magically materialize. Adjusting the boundary between noise and silence, she projected her voice so that it echoed throughout the entire residence and grounds.

"Chen, could you please come back to the veranda?"

She knew that Ran's shikigami would be present; the tasks she'd set Ran were ones where the kitsune wouldn't bring Chen along with her, and Ran being Ran she would have assigned Chen certain tasks of her own to keep the nekomata from getting into too much trouble when unsupervised.

And yet, Chen did not appear.

"Chen?" Yukari raised her voice slightly, not actually all the way to "miffed" but somewhere past "curious." The patter of tabi-clad feet on the floorboards followed, and the youkai cat burst out through the doors.

"I'm sorry, Lady Yukari! I didn't hear you at first!"

"Ran is keeping you busy in her absence?"

"Uh-huh." Chen pouted. "She has me doing math problems."

Yukari blinked.

"Well, mathematical ability is necessary for a shikigami to properly fulfill her functions, so it's good that you're practicing."

"Yeah, but these are hard!"

"Perhaps I can be of help? Why don't you let me take a look at what you're doing…and you can prepare a pot of tea while I'm doing that. Perhaps the Darjeeling would suit."

Chen brightened at the offer.

"Yes, Lady Yukari!"

She scurried back into the house, then came right back with a piece of paper. Handing it over, she disappeared back into the building again. Curious, Yukari looked down at the page.

Five human bank robbers in the outside world flee the police into the forest near the Hakurei Shrine and stumble through the weak point in the Great Hakurei Barrier beneath the third cherry tree past the fourth maple that's been widening for months. Two of them really enjoy grilled lamprey, so they follow the smell to Mystia's stand and buy several skewers, for which they are safely guided to the Human Village. One robber follows the road successfully to the Hakurei Shrine and is returned to the outside world. The remaining two robbers blunder to the shore of Misty Lake. Remilia is feeling hungry and happens to attack and nearly drain one, who is later found unconscious by Reisen and brought back to Eientei for treatment. The final robber runs off into the woods in terror. Assuming a start time of 2:30 a.m. and that the robber is an adult male in typical health and the equivalent level of stress that a Gensokyo native would feel under the circumstances, calculate how dense the forest would have to be so that there would be a 75% chance Rumia would continue to crash into trees until dawn rather than be able to successfully catch and eat the last outsider.

Yukari smiled wryly, tweaked the boundary between knowledge and ignorance to print the calculations for the answer for Chen on the bottom of the page, and rose to her feet.

"Well played, Ran," she said, and flew away to shore up the weak spot in the barrier.