In my research for a school project, I've stumbled across a modified twin paradox here.

It apparently seems to violate special relativity, yet I cannot find any faults in the argument with my current knowledge (admittedly not a lot, but I've read about the original twin paradox).

I have searched the internet for an answer, but there seems to be nothing written about this. As it is the holidays, I am unable to ask my teachers. So can someone provide an explanation or refutation (for my interest)?

Any help would be appreciated.