Then the king said, 'One says, "This is my son that is alive, and your son is dead"; while the other says, "Not so! Your son is dead, and my son is the living one." ' So the king said, 'Bring me a sword', and they brought a sword before the king. The king said, 'Divide the living boy in two; then give half to one, and half to the other.' But the woman whose son was alive said to the king—because compassion for her son burned within her—'Please, my lord, give her the living boy; certainly do not kill him!' The other said, 'It shall be neither mine nor yours; divide it.' Then the king responded: 'Give the first woman the living boy; do not kill him. She is his mother.' All Israel heard of the judgement that the king had rendered; and they stood in awe of the king, because they perceived that the wisdom of God was in him, to execute justice. (NRSV 3:23-28)
Then said the king, The one saith, This is my son that liveth, and thy son is the dead: and the other saith, Nay; but thy son is the dead, and my son is the living. And the king said, Bring me a sword. And they brought a sword before the king. And the king said, Divide the living child in two, and give half to the one, and half to the other. Then spake the woman whose the living child was unto the king, for her bowels yearned upon her son, and she said, O my lord, give her the living child, and in no wise slay it. But the other said, Let it be neither mine nor thine, but divide it. Then the king answered and said, Give her the living child, and in no wise slay it: she is the mother thereof. And all Israel heard of the judgment which the king had judged; and they feared the king: for they saw that the wisdom of God was in him, to do judgment. (KJV 3:23-28)
So is the woman who gets the baby the actual, biological mother? Or does Solomon just want to give the baby to the woman who will care the most for it, regardless of who the "real" mom was? And what would he have done if they had both reacted identically one way or the other?