Different outcomes depending on various factors...
The silly answer would be: She would melt.
But if we put some effort into it...
The underground would not have been introduced, the game would probably be centered around misty lake,
Cirno would become a master of Cold Fusion, the entire incident would be based on how she could finally
show everyone that she is "The strongest", spawn way more jokes about "Being the Strongest", turn Daiyousei
into an EX-Boss and transform the lake into a hotspring in the end.
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What if... Rinnosuke was a playable character?
Flat answer will be that he would lose every duel [b/c no spellcard] but if we made things a little more creative...
Touhou 14: Impossible Mechanics
>Select playable character
>Flandre
>Shot: "Kyuu~" everything in existence
>Reimu
>Shot: Homing Amulets
.
.
>Rinnosuke [Auto Lunatic on all stages] >>SELECT
>Shot: What do you mean, shot?
>SpellCard: What do you mean, SpellCard?
Stage 1: Implausible attempt of the powerless shopkeeper
>Tries to fly
>Realises cannot fly
-DUE TO THE CHARACTER BEING UNABLE TO FLY, THE STAGE IS LENGTHENED. RINNOSUKE HAS TO WALK.-
>Shot by Fairies
>Tries to deathbomb, until you saw the "Nullify" sign on your bombs
>Loses 10 lives in rapid succession, and clicks on "Continue" 29, 995 times.
>Reaches Boss
Rinnosuke: Give... me... a... break...
Cirno: あたいは『馬鹿』じゃいないもん!あたいの『力』を見せる!
Rinnosuke: WTFLOLWUT I do not understand---
>Subsequently killed by Cirno's Icicle Fall -Easy-
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On a serious note, I would like to see him flying around with a airborne system, using a electric shikigami to pilot the system, and having affixed mini-hakkeros on that thing as a combat machine. Perhaps his bomb would be a shot from a Hakkero [We never seen the non-mini-hakkero ever].
Perhaps he would be using ballastic weapons! [Rinnosuke with a Sub-MachineGun, anyone?]
But he would be a sad man. He would end up like how Cirno ended in Cirno's Perfect Math Class, with all those bullets, Yin-Yang orbs and knives all over him.
>Continue
>Return to Title [SELECT]
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What if Patchouli was as powerful as MeiLing on physical terms, and retained her prowess over spells?