Ok i cheated to get the answers... it made no sense from the clues we got @_@ what kind of theroy do they want me to build? i got 1 of 3 correct... but the rest? am not going to go into it because i will sound to mean... but this kind of puzzles reminds me very well of the zero escape ones where they creator of them make one theory in his head and expect you to reach it also, even when you can reach multiple different ones with what you get @_@
So right now... i think it's kinda obvious that they have swapped each other... Ringo was the one who was gone and Ichigo was with us the whole time... why? i think it's because of the books being untouched by her even though Ringo loves them @_@ So... why did she escape?... i think it's because when Mayuri and Ringo were in the same room... something between them happened @_@ and the twins are trying to help each other achieve something...