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I think it's kind of odd how Matsurugi is involved. Why would he have a baseball bat... in a hospital? Why would Matsurugi's destiny be affected by the skull, but not the other e-test participants (bar Sumio and Shigeru)? It's not like his ability is the most useful. Why would he know about Cannibal being able to take on other peoples' appearances? He seemed surprised by the corpse, so he probably didn't put it there on purpose. It's possible that the Enigma skull warped Cannibal's destiny by putting Matsurugi's corpse on the train (so Sumio will... eventually figure it out). It's also suspicious how Matsurugi wasn't in the "Someone is... Cannibal...!?" splitscreen. Sakaki definitely tried to draw attention away from him.
Nice theories. The parts I highlighted in bold really got me.
As for my theory of the test, I believe that the murderer will be the first to go. He's not Cannibal. What kind of a plot twist would that be? A murderer ending up being a murderer. Go figure, right? He's just a filler character made to show how the stakes are higher in this test. The girl will be second to go. After that we will find out that Matsurugi is Cannibal, and he will be the third to go. Safe Man and Sumio will be the final two, and we'll find out that Safe Man is Sumio's dad. Sumio will naturally be the one to make it to the island.
I don't know how Shigeru or the disappearance of the city will tie into this arc. Sakaki is a really good author, though, so I'm not worried.
In increasing order, here's how screwed up I think the three new characters may be:
1. Mao Nanafushi (the girl)
I think she's the true filler character. Her ultimate wish to murder some of her classmates sets the bar pretty low on how screwed up the new characters may be. That is, I think she'll turn out relatively unimportant compared to Akame and the Safe Man, who may be after much worse things.
2. Tsutomu Akame
He's a convicted murderer with his murderous intent seemingly unchanged, as proven when he took Sumio hostage. He can't possibly be up to any good.
3. The Safe Man
He's already proven himself to be two-faced with his classy arrogance. With no descriptions on his background and few words or actions coming out of him, there's no limit to how potentially screwed up he may turn out to be later in the story.
Based on that, I'm predicting the order of elimination would go like this:
1. Mao Nanafushi
2. Tsutomu Akame
3. Jiro Matsurigi
4. The Safe Man
Basically, the more screwed up the participant, the more likely they'll stay on the train longer because there's more character development that can occur within them through the test. I'm predicting a one-on-one fight in the last challenge with Sumio and the most screwed up character of them all, the Safe Man. I'm also going to assume Sumio wins the challenge. That's why I rank Matsurigi second last eliminated.
Of course, with the nature of this manga, I can explain many other possibilities with plausible theories out of the blue for each and it would have just as much of a chance occurring instead.