Jesus and the 3 Wise Guys

Have you ever noticed that the Bible doesn't specifically say how many wise men showed up in Bethlehem? We're told that wise men from the East followed a star, interacted with Herod, and made their way to the manger (bearing gifts) but nowhere does it say how many men there actually were. So, how exactly did this idea of the 'three magi' begin if Matthew 2 doesn’t give an explicit number? Is this just the byproduct of an overzealous songwriter thinking that 'We Three Kings' sounded better than 'A couple of Kings' or 'About Four Kings'?