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Icarus personal challenge is his playful manner that leads him to death because he forgot his father's instruction how to fly using the invented wings. Another challenge he needs to supposedly overcome if he hadn't die is King Minos who was very angry at them On the other hand, Daedalus personal challenge is his talent and skills in invention and crafting that made him do a lot things without proper judgment of its advantage and disadvantages that sometimes puts him in trouble. He also needed to overcome King Minos who hadn't stop searching for him. And of course the nephew he killed, Talos.
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