Disclaimer: I do not own Naruto.

Geometric Proofs

A geometric proof is a list of reasons or rules used to prove a mathematical concept is correct. They're like logic puzzles. Another way to look at them is as a problem that comes with a bunch of conditions that must be met. To solve one, the challenge is to obey the conditions by either finding a way to work around them or using them in your favor.


"Finished already?" Lord Hokage asked around his pipe. The mission hall was quieter than I was used to. Less foot traffic as people came and went. Which might be related to the stacks of scrolls sitting on the corners of the mission desk. A chunin sat on either side of Lord Hokage; trying to keep everything organized.

I shrugged; not understanding the Hokage's surprise. It wasn't like delivering groceries was difficult. The client only ordered enough ingredients for two meals. Besides, one saves time when traveling by hopping rooftops and using chakra to go faster. As much as I hate to admit it, learning enough chakra control and building enough endurance to travel like that was probably the best part about being a ninja.

"Very well", Lord Hokage moved on after a lack of a verbal answer. He handed the mission scroll to the chunin on his right so it could be marked as complete. "For your next mission, Madam Shijimi's cat has gone missing ag-"

Holding up a hand, I interrupted the Hokage; gaining scandalous looks from the chunin aiding him at the mission desk. "Only give me that mission if you want Tora to come to an untimely demise".

The chunin on the left gasped. While the one on the right started grumbling about the audacity of genin these days. How dare I speak to Lord Hokage like that. But they didn't get it. They didn't know that by appeasing Danzo, Kabuto's mind was still a fortress of secrets. And the looming invasion was still an unknown. If only Lord Hokage had stood his ground. Then the Sand would already be exposed. The higher-ups wouldn't think Orochimaru was only in the village for Sasuke. And… Lord Hokage might not have to die.

A puff of smoke left the Hokage's pipe as he studied me; the corners of his lips curling up in amusement. Almost as if he was considering the consequences of letting me kill the noblewoman's cat. On one hand, Madam Shijimi would be pissed and he'd have to deal with an unhappy and somewhat influential customer. On the other hand, no more 'find Tora' missions. Honestly, the other genin might name me a hero if I took care of that furball.

"How about a C-rank instead?" The Hokage proposed.

Scowling, I placed a hand on my hip. It was bad enough I was barred from T&I for the foreseeable future. Did he really have to punish me with a C-rank on top of that? Though the way the chunin were reacting, you wouldn't think it was a punishment. "Lord Hokage!" The one on the left protested. "If the brat can't even handle finding a missing pet, is a C-rank really appropriate?"

The Hokage continued to smoke his pipe. "D-rank missions are still piling up", agreed the one on the right. "And we don't have anyone to go with her on a C-rank".

"Rion will be fine", the Hokage assured them. Though I beg to differ. "Besides, for this C-rank she won't have to leave the village".

Narrowing my eyes, I stared at the Hokage. That didn't sound right to me. What C-rank could happen without needing to leave home? Though the two chunin seemed to catch on. They relaxed in their chairs and sported placated grins. "Oh, you mean that mission", said the one on the left.

My scowl deepened. This didn't sound good.

"There's been an increase in complaints about inappropriate behavior at the Konoha Hot Springs. As such, the owners have asked for a shinobi to guard the outside of the women's bath to discourage less-than-savory behavior", said the Hokage. His pipe never left his mouth.

A bird flew past the windows as I thought. So… the mission was to scare the crap out of any peeping toms. And I'd get paid at a C-rank rate? My hand dropped from my hip. "When you say discourage, does that mean I can use force?"

"Only if appropriate", The Hokage answered. There was a certain gleam in his beady little eyes that I was having a hard time reading. It didn't feel like it should fit the context. "I expect you'll remember Konoha's rules while dealing with civilians. However, if this behavior is being done by a shinobi, by all means, do what you feel you must".

The two chunin had matching grins on their faces. Lord Hokage seemed a little too pleased. What weren't they telling me? But still, thinking about all the creeps Anzu had to deal with throughout the years, this sounded like a mission I might actually enjoy. "Fine", I relented. "I'll take it".


Standing in front of the tall wooden fence that separated the women's bath from the main street, I listened to the sounds of splashing water and the occasional giggle as I felt the steam from the hot spring on my skin. I'd never been here before. Walked past, sure. However, I've never been to the Konoha hot springs. I think Shibi offered once or twice. He and Shino liked to visit once in a while. But I was happy with the privacy of a single-sized bathtub behind a locked door. It was easier to relax that way. Though maybe it was time to reconsider. Anzu might like it. And it wasn't like we'd be denied entry anymore.

It was turning out to be a low-key mission. I got to the bathhouse an hour ago. There were no peeping toms when I arrived. And none have appeared since. So, all I've been doing was standing and waiting. Maybe just having a ninja standing here was enough of a deterrent.

But being so still and silent meant I had time to think. Fidgeting with the ends of my braid, I did just that. After talking with Shikamaru yesterday, I walked away with three key facts:

1. Both Team Ten and Team Seven already knew about Orochimaru.

2. The team from Sound died in the Forest of Death.

3. The preliminaries didn't pan out as I remembered.

Though the why, how, and specific details were still foggy. Somehow, Ino made it through the preliminaries but Neji had not… It was a struggle to wrap my mind around that one. I needed to ask more questions. Talk to more people. Or better yet, maybe I could read the witness statements from those summons I delivered yesterday. That would be less suspicious… If I didn't get caught. You know, since T&I was currently off-limits.

"Hey. Hey Miss?"

How do I move forward from here? What would follow? Either way, it didn't affect me if Sasuke defected from the village. The only thing I needed to worry about right now was the invasion. If that could be controlled or avoided, then Anzu would be safe.

"Excuse me, young miss?" A voice breathed into my ear. Goosebumps littered my flesh as tiny hairs on the back of my neck stood on end. I hadn't seen, heard, or sensed anyone approaching. Why? Snapping my head to the left, my eyes stretched as wide as possible. Squatted next to me, but somehow just below eye level, was a behemoth of a man with flushed cheeks and a dopey smile. He had crazy spikey white hair that was longer than mine. Probably even longer than Haku's. And two red lines ran down his face. Almost like tear stains. "Do you mind moving aside? There's some very important research I need to do".

Oh. My hands curled into fists and my eyes returned to normal. This clown, I recognized. Suddenly, the reason this mission was a C-rank became a lot more obvious. "Not happening", I said over the background noise of splashing and giggling. Though the ambiance only added more color to the old man's face.

"Come on", the man pleaded. "I'm a very successful author. But only because my descriptions are accurately lush and vibrant". He kept wiggling his fingers as if tickling the air. "To maintain a high standard of writing I must view young and beautiful ladies whenever possible". There was drool crawling down from the corner of his mouth. "You know, ones with full lips. Big-"

The man cut himself off in time to intercept the kick I aimed at his head. As his whole hand wrapped around my ankle, I started building chakra. "Lord Hokage told me to stand in front of this bathhouse to stop assholes like you. My guess is he knows you're in the village".

"Heheheheh", he chuckled; using his free hand to wipe away the drool. "So, you know who I am". The fingers of the hand holding my ankle started squeezing and rubbing certain spots along the joint. My skin crawled. "But that means you also know, my dear, that there is no stopping the great and mighty Jiraiya, the Toad Sage!"

At his obvious pride and lack of shame, my left eye began to twitch. Hatred was useless. Especially when indifference was a much more effective tool. But I'm willing to make an exception for this lech. Pushing my chakra out of my body and away from my person, Jiraiya was pushed back. He let go of my ankle as he was forced away; wooden shoes screeching against the stone path. Though, since he was a huge whole person, my chakra could only push him so far.

Releasing this technique I still haven't named, some of my chakra came back to me. Some of it didn't. "That was a good try, little girl", Jiraiya goaded; all play without an ounce of seriousness. "An interesting party trick". In a blink of an eye, Jiraiya rose to his feet and started gesturing with his arms. "But it's not enough. Nothing will ever be able to pull a true master away from his art". Jiraiya kept fluctuating his tone in the middle of his sentences; going high or low to emphasize different words.

It was annoying. Even more so than Gai's theatrics. "There's nothing artful about spying on women", I yelled back as one of my fingers hooked through the looped handle of a kunai knife and pulled it free from its holster.

In the background, the splashing stopped. "What was that?" Someone, a woman, asked. "Did someone say we're being spied on?"

"Maybe we should go home early".

As I gripped my kunai and held it at the ready, Jiraiya's flushed cheeks cooled and he began to frown as his arms came to hang limply at his sides. I wasn't stupid. I know there's no way I'd be able to do any damage to a sannin. But it was also safe to try. As disgusting as Jiraiya's vices were, he wouldn't hurt a genin from his own village. Meaning, I was free to use him as target practice and shout as much abuse as I wished.

"Now look what you've done", Jiraiya complained; pouting like a spoiled child. "You scared away all the pretty ladies. And I didn't even get to take one peak". Scared? It took some effort to not grip my kunai tighter. More like warned if you ask me.

"Pervy-Sage!" Naruto screeched as he raced into the scene. "There you are. I've been looking all over for you. You promised to help me with my training. Remember yesterday?" Naruto came to a halt between Jiraiya and me; his back towards the steaming water. He waved an accusing finger in Jiraiya's direction. "But all you've done since this morning was stare at girls in their bathing suits! And now I find you back at the bathhouse with Rion looking like she wants to kill you and… and…" Naruto's brain caught up with his mouth.

Blinking he lowered his pointed finger and turned his head towards me. "Hey, Rion. Why are you here? The Pervy-Sage didn't do anything to you, did he?" Jiraiya seemed even more disheartened by Naruto's appearance than he was by the bath becoming vacant.

I lowered my kunai with a heavy sigh. So much for target practice. Before I could reply, Naruto guessed at the answer. Refocusing back on Jiraiya, Naruto raised both his fists to be close to his face. "It's bad enough you're crazy for the ladies, but don't bring my friends into it".

Jiraiya let out a self-pitying sigh, but it wasn't enough for Naruto to take the hint.

"I don't care if you are going to teach me a super cool jutsu. If you hurt my friends, I'll pulverize you!"

Something complicated stirred inside of me. The feeling was foreign and it made me want to hide. "Give me a break, Naruto", Jiraiya whined. "Any friend of yours is way too young for me. Just look at her". Maybe I lowered my kunai a little too soon. "She could pass as a boy if she had to".

Naruto shook a fist at him. "Pervy-Sage!"

My ears picked up the sound of approaching footsteps; sandals scuffing stone. The fact I had, told me it was a civilian. "Naruto? Rion?" A concerned voice made herself known. "Is everything okay?"

Anzu slid into place next to me; her arm slid behind my shoulders in a silent claim that she hadn't needed to make in a long time. The fact she felt the need to do so now made my chakra bubble uncomfortably.

Naruto lowered his fists as he turned to look at my sister. "Anzu Nee-Chan, what are you doing here?" He sounded genuinely surprised to see her. Other than the one time she saw us off for a mission, I'm not sure he's ever seen Anzu outside of our home or when they went out for ramen. Though… a thought occurred to me. When did he start calling Anzu big sister?

"I had the day off", Anzu replied nervously; eyes flashing over Naruto. But experience taught her not to look away from Jiraiya for too long. I dug my fingernails deep into the palms of my hands. "Gai mentioned how good it was for recovering to take a long soak, so I thought I'd see if I could buy a pass or something… for Rock Lee".

"That's a great idea", Naruto agreed as Anzu gave my shoulder a squeeze. Jiraiya hadn't looked away from Anzu once. His mouth hung open with a slacked jaw. An almost longing quality sparked behind his eyes.

I tried not to do the math. I tried very very hard. "But why are you and Rion here?" My sister used the corner of her eyes to study the side of my face. "Are you okay?" She asked both of us.

Anzu was doing a much better job ignoring the staring sannin than I was. When his staring became too much, Anzu tucked a strand of inky black hair behind her ear and ducked her chin; revealing the roots that were starting to show. She dyed her hair black twice in a row. I thought the choice had something to do with Gai. Like she was trying to match him or something.

"Yeah, we're fine", Naruto answered. He turned his back completely to Jiraiya; his whole posture relaxing. "I'm just here to track down this old geezer so I can finally get some training done and Rion… Why are you here?"

Sighing, I tore my eyes away from Jiraiya to give Anzu my attention. "I got assigned to protecting the bathhouse from jerks trying to steal a peak".

Anzu's eyes widened at my answer as Naruto teased his new teacher. "Hear that, Pervy-Sage? Old man Hokage must be on to you".

"But…" Anzu worried; her eyes giving Jiraiya another once over. His mouth was no longer open. It was a slight improvement. "The type of people who would do that… I signed you up for the academy so when you grew up you wouldn't have to deal with these sorts of things".

I opened my mouth to respond. Anzu didn't need to worry. Her plan had worked. Even if it hadn't been what I wanted. Donning a headband meant there was a lot I didn't have to do if we had stayed in the red-light district. Better even, it meant I had the skills to fight back. But Jiraiya spoke up before I could get any of that out. "Let's go, Naruto".

"Huh?" Naruto asked as he turned his head to look at the Toad Sage.

"When there's still daylight. You said you wanted to train, right?"

A broad grin bloomed across Naruto's face. It nearly drowned out Jiraiya's mask of indifference. "Alright! Now that's what I'm talking about". Naruto ran off, calling over his shoulder, "See you at home. Rion. Anzu Nee-Chan. Maybe we can have ramen for dinner!" Jiraiya followed.

For a few seconds, Anzu and I stood in front of the bathhouse. Her arm still wrapped around my shoulders as we breathed in the steam and scent of the hot spring. "Rion, that man-" Anzu started to say.

"Sis, please don't". I interjected. That life was behind us now. We both had respectable jobs. Anzu was getting closer and friendlier with Gai. There was no reason to revisit the old us.