The rabbis of the Talmud were bothered by a contradiction: the book of Kings describes Saul as killing every Amalekite, and yet Haman, according to his pedigree in the book of Esther, was an Agagite, a descendant of the Amalekite king. The Talmud offers an instructive solution: after Saul had killed every Amalekite, he experienced a moment of mercy, and wrongly refrained from killing King Agag. This allowed Agag a window of opportunity; he had several minutes before he was killed by the angry Samuel. In those precious moments, Agag engaged in relations with a random woman, and his progeny lived on to threaten the Jews in the future.
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