Did Saul and Samuel kill all the Amalekites?

Yet, we read that Agag’s mother was left alive (I Samuel 15:33), David killed the Amalekites later (I Samuel 27:8-9), David killed more again (I Samuel 30:1, 17), and Saul was killed by an Amalekite (II Samuel 1:8-10).

Response

No, Saul and Samuel did not kill all the Amalekites.  The Bible says Saul killed only the Amalekites “from Havilah until thou comest to Shur”.  Those Amalekites outside this region were not killed, nor were the ones who escaped David’s two subsequent attacks.  Saul was actually not killed by an Amalekite—Saul killed himself, and this Amalekite was lying.  Nonetheless, Haman in Esther was a descendant of Agag the Amalekite king, and so the Amalekites were not completely destroyed.