How Could Merlin Possibly study in Slytherin House Centuries Before it Was Founded?
This is not a duplicate of questions about Merlin's biography in Harry Potter like In Harry Potter, Who is Merlin?: it is asking how Merlin could have possibly studied magic in Slytherin House.
To all of us Muggles, the most famous wizard of all was Merlin, the wizard at the court of King Arthur, a wizard who was active centuries before Hogwarts and Slytherin House were founded.
The character of Merlin in all medieval romances is based on the character of Merlin in Geoffrey of Monmouth's Historia Regum Britanniae, circa 1135. Geoffrey in turn based Merlin on at least two legendary and possibly historical men, Aurelius Ambrosius and Mryddin.
According to the Historia Brittonum, circa 832, Aurelius Ambrosius was a king of the Britons in the 5th Century AD. Geoffrey includes Aurelius Ambrosius as a King of the Britons, but takes the story about Aurelius Ambrosius as a magical boy confronting King Vortigern and adds it to the biography of his wise man Merlin.
According to Welsh legend (and possibly history) Mryddin was a British warrior and seer in north Britain who went insane and live as a wild man in the woods after his lord was killed at the Battle of Arthuret about 574 AD. Geoffrey took a few details from the legend of Mryddin and used them for his Merlin.
So Merlin is more or less based on two different men, who lived in different parts of the period from 400 to 600 AD.
Furthermore, Merlin is famous as being a wise man and/or wizard at the court of King Arthur. The Annales Cambriae, circa 975, say that Arthur won the Battle of Baden in a year corresponding to 516, 517, or 518, and was killed at the Battle of Camlann in a year corresponding to 537, 538, or 539. Geoffrey of Monmouth's Historia Regum Britanniae, circa 1135, dates the Battle of Camlann to 542 AD.
Arthur is also famous for leading the Britons against the invading Angles, and Saxons, and Jutes (oh my!) and so has to be dated before about 600 AD when they already ruled all of southern England.
So anyone who knows anything about British history, legend, and chronology associates Merlin the Wizard with the 6th century AD, when he did all his famous deeds. Merlin could have used magic to live for centuries or millennia after that date, but he isn't famous for doing anything great after the 6th century so would have lived quietly and out of sight in later centuries.
But it is claimed that Merlin was a graduate of Hogwarts and Slytherin House, though Hogwarts wasn't founded until centuries after Merlin gained his fame.
In his answer here LCIII quotes Pottermore:
"Here’s a little-known fact that the other three houses don’t bring up much: Merlin was a Slytherin. Yes, Merlin himself, the most famous wizard in history! He learned all he knew in this very house! Do you want to follow in the footsteps of Merlin?"
Merlin's famous wizards cards say:
Medieval, dates unknown Most famous wizard of all time. Sometimes known as the Prince of Enchanters. Part of the Court of King Arthur.4
Merlin is the most famous wizard of all time. He is sometimes known as the Prince of Enchanters and was part of the Court of King Arthur.
But I don't know if this is canon, or what details about Merlin's biography in HP sources are canonical.
Is Merlin in Harry Potter supposed to have lived backwards in time like he did in The Once and Future King?