My "take" on the Star of Bethlehem is somewhat different from the usual story.
I suspect there was some natural phenomenon that God gave men the perception to see, that compelled some of them to investigate, coming from all corners of the then known world. I don't think the wise men traveled together (unless at the very end of the journey); I suspect they were a motley collection of lone wolves who were curious.
And there were probably more than three of them.