Thirty Nine
ICON VERSUS MEME:

"Make a list of all the characters in your icons. (Although you may have more than one icon of a single character, they only go on the list once.) Alphabetize it. Take the first two people on the list; that's your first pairing for battle. Second two people; second pairing for battle. Etc. Then write your reaction to each battle."

Caterina Sforza // 2
Chikane Himemiya // 4
Patchouli Knowledge // 11
Yuriko Kuraki // 18
Celine Jules // 3
Seth Nightroad // 15
Kanako Yasaka // 7
Schala Zeal // 14
Utsuho Reiuji // 17
Rena Ryuuguu // 12
Arcueid Brunestud // 1
Chikaru Minamoto // 5
Satori Komeiji // 13
Nikola Tesla // 10
Mika Ayanokouji // 9
Kaon // 8
Shana // 16
Inara Serra // 6

ARCUEID v. CATERINA
CELINE v. CHIKANE
CHIKARU v. INARA
KANAKO v. KAON
MIKA v. NIKOLA
PATCHOULI v. RENA
SATORI v. SCHALA
SETH v. SHANA
UTSUHO v. YURIKO

#1 -- Arcueid Brunestud vs. Caterina Sforza
//
Let's face it... Caterina's not all that much of a fighter. However, I doubt that Arcueid has much reason to get into a fight with Caterina unless it were initiated otherwise, and Arcueid probably doesn't seem like an enemy to Cat that much. Of course, if they did fight, Arcueid is just a little too powerful for almost anyone to take on.
WINNER: Arcueid.

#2 -- Celine Jules vs. Chikane Himemiya
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Since Celine has her magic, and is very good with it, she would probably more than stand a chance against Chikane, but, were there no magic used, Chikane is extremely capable and would have little to no trouble with a Celine stripped of her magic.
WINNER: Celine, most likely.

#3 -- Chikaru Minamoto vs. Inara Serra
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There likely wouldn't be one. In fact, the end result would probably be that they'd end up as good friends... in several ways.
WINNER: fffffff

#4 -- Kanako Yasaka vs. Kaon
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Hm... Mostly indestructible girl who turns into a death machine versus wind god? Would probably go on forever. But Kaon would need Himiko for the energy, thus...
WINNER: Kanako

#5 -- Mika Ayanokouji vs. Nikola Tesla
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Depends on the Nikola Tesla we're working with here; he varies from being a super-cool scientist to being a god. As a scientist, he probably possesses some awesome machinery that would easily down Mika, and as a god, no question here, Tesla would whoop ass.
WINNER: Nikola motherfucking Tesla.

#6 -- Patchouli Knowledge vs. Rena Ryuuguu
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Rena mat be bat shit crazy, but Patchouli has real power; she is one of the strongest mages in a game which includes mid-ranked characters who can level mountains with one spell. YEAH UM.
WINNER: Patchouli

#7 -- Satori Komeiji vs. Schala Zeal
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I doubt either of them would get into a fight, though Satori's not the nicest mind-reader ever, so she might start something. Is Schala more powerful than Satori. Possible. Especially if she carries the Time Devourer with her...
WINNER: Schala

#8 -- Seth Nightroad vs. Shana
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I don't know what the hell to do with this one. I suspect that, were there a fight, it would be very, very protracted, and might not even have a winner.
WINNER: No idea.

#9 -- Utsuho Reiuji vs. Yuriko Kuraki
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For as evil as Yuriko is, she is still likely susceptible to radiation, and Utsuho has the power to induce nuclear fission/fusion. Can't see this being too pretty...
WINNER: Utsuho.