It doesn’t say the words “three gifts.” The second chapter of Matthew states, “Then Herod secretly called for the wise men and learned from them the exact time when the star had appeared. Then he sent them to Bethlehem, saying, ‘Go and search diligently for the child; and when you have found him, bring me word so that I may also go and pay him homage.’ When they had heard the king, they set out; and there, ahead of them, went the star that they had seen at its rising, until it stopped over the place where the child was. When they saw that the star had stopped, they were overwhelmed with joy. On entering the house, they saw the child with Mary his mother; and they knelt down and paid him homage. Then, opening their treasure chests, they offered him gifts of gold, frankincense, and myrrh. “ You’re correct. Each of the 15-18 wise men might have given one container of gold, frankincense, or myrrh. If that happened, Jesus would have received 15-18 gifts.
That is a possibility--one gift per person. But it does not say one gift per person. Each person could have given many gifts or none at all. For example, wise man #1 could have give two gifts of gold. Would the gifts have been in the form of bouillon or rings or bracelets? It does not say. So take your pick.
But to limit each person to only one gift is reading specifics into the text that are not there. It does not say how many gifts each gave.