This one might seen weird and out of nowhere, but what if Blackbead is also a descendant of the Three-Eye Tribe like Pudding?
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1– He always has something covering his forehead (and keep in mind Pudding could hide her third eye with just her hair), we literally never saw Blackbeard’s forehead completely.
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2– Pudding had some type of multiple personality disorder, that was very clear when she gets confused about her feelings for Sanji. A common theory about Blackbeard is that he has 3 different personallities (or souls), what if the multiple personalities thing is a characteristic of the Three-Eye Tribe people?
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3 – Three-eyes possess the potential, with their third eye, to achieve “true awakening”, which supposedly comes with the ability to hear the “Voice of All Things” — thus giving three-eyes potential to decipher and read Poneglyph writing. It wouldn’t be that far of a stretch if they also could consume 3 devil fruits, maybe Pudding just don’t know she can do that yet, or maybe it requires said awakening, which in this case Blackbeard would have.
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It’s stated by Oda that Blackbeard likes to study history, if he really has the power of the Three-Eye Tribe that would be quite easy for him to collect a bunch of information, since it appears that they can use some sort of “Voice of All Things” power.
*Theory by Shedinjask