"We must've been through hundreds of books already and we can't find him anywhere —"
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The Head of Hufflepuff house is a professor at Hogwarts School of Witchcraft and Wizardry with the special obligation of looking after the students of their house: Hufflepuff. It is unknown how a professor would be elected for the post, but it's most likely that the headmaster chooses the professor whom embodies all the qualities Helga Hufflepuff herself had (loyalty, kindness, generosity, etc.) and probably was in Hufflepuff House when he/she was in Hogwarts.