1 Kings 3:23-24

1 Kings 3:23-24 King James Version (KJV)

23 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.

24 And the king said, Bring me a sword. And they brought a sword before the king.

An American English Bible
With Old Testament based on the Greek Septuagint

23 Then the king said to them: 'You're saying that the living son is yours, and the dead one is hers. And she says that's not true; hers is the living son and yours is the one that's dead.' 24 So the king said, 'Bring me a sword!' And they brought him a sword. 25 Then he said, 'Cut this living, nursing child in halves, and give half to this one and the other half to that one!'

These are my thoughts, please share yours.

23 So the king sees that the both claim the living boy as their own and claim that the dead one belong to the other. There was no way of proving this at such a young age the baby may not have developed to look like his mother as much.

24 The ordered to have a sword brought to him to had to listen to their king some kings may have resolved the problem by killing the baby, so this may have been what he could do. Our sword is the word and we need to keep and look at it when we have a decision to make.
Yes, the word is sharper than any double-edged sword and is a lamp unto our feet: the word helps us discern the paths God wants us to take, to be sure.

What I find noteworthy about this passage is how it comes right after Solomon asks for an hearing/perceiving heart so that he can perceive justice to carry out his responsibilities as king, and judge God's people:

8 Your servant is in the midst of your people which you have chosen, a great people, that can’t be numbered nor counted for multitude. 9 Give your servant therefore an hearing/perceiving heart to judge your people, that I may discern between good and evil; for who is able to judge this your great people?
Then, peased with his selflessness, God gives Solomon riches, honor, and wisdom as well, and promises a long life if Solomon walks in His ways, as David did. Our requests can be very pleasing to God if our heart is set on serving Him.
Then with the women and boy (3:16-28), the wisdom/understanding God gave Solomon to give justice is applied in this case of a wronged prostitute, underscoring God's concern for all His people. If we set our heart on serving God, He will set His heart on pleasing us.