The Dancing Princesses1987

A king with six daughters who is extremely over protective locks them in their room at night. But for some reason they order shoes from the cobbler practically every day and the king has to pay for them. And when he ask them why, they don't give him a straight answer. So he sends word that whoever figures out why they need so many shoes, he will have the hand of the daughter of his choice. But so far none have succeeded cause they make sure no one can find out. But a soldier upon learning of this decides to find out after being given a cloak that renders him invisible.