The parable of the flute

While I was reading about environmental justice, I came across the parable of the flute that the Indian philosopher, Amartya Sen, mentioned in one of his books. The parable is about a flute which is found in a village. More than one child claims it's theirs. Ann claims it's hers as she's the one who made it while Carla wanted it to be hers because she plays the flute well. On the other side, Bob thinks the flute should be given to him as he's the poorest child and he doesn't have any toys to play with.

In my view, it's a complicated situation. To whom should the flute be given? What is the fair and just thing to do in this situation?
For some people, without Ann and her skills in making such an instrument, there wouldn't have been a flute. The person who made the flute should own it or at least decide on their own to give it away to someone else. This is a symbol of libertarianism which adopts the idea of protecting ownership.
A different view might say that by giving the flute to Carla, she can give the village's people pleasure by playing the flute for them. This reflects prioritizing achieving the greater benefit and good for the majority, in philosophical terms, it's utilitarianism.
Others might request the flute to be given to Bob in an attempt to reduce the wealth gap between the different individuals. This represents the concept of egalitarianism.

In every scenario, only one child will be pleased and others will feel displeased and will think they have been treated unfairly. I think there's no such thing as the correct thing to do for everybody. What is just and fair for you, could be unfair for others. What could bring benefits for you, could cause trouble for others. It's why the conflicts arise without end in this world.