a seemingly impossible decision that has to be made between competing alternatives; a wise decision that has been made in response to a seemingly impossible choice
—When Joe’s mother realized she was allergic to his dog, Joe was faced with the Solomon’s choice of moving away from his family or giving away his beloved pet.

After Solomon became king of Israel, God told him in a dream to ask him for whatever he wanted. The new king described himself as a small child ruling over a huge number of people, and said,

So give your servant a discerning mind so he can make judicial decisions for your people and distinguish right from wrong. Otherwise no one is able to make judicial decisions for this great nation of yours. (1 Kings 3:9)

Pleased with Solomon’s request, God responded,

Because you asked for the ability to make wise judicial decisions, and not for long life, or riches, or vengeance on your enemies, I grant your request, and give you a wise and discerning mind superior to that of anyone who has preceded or will succeed you. (1 Kings 3:11,12)

A ruling made by Solomon gives an example of his wisdom: Two prostitutes, who lived together, came to him. Each had given birth to a son, with the two boys born a few days apart. One night, one of the babies died, and each woman claimed that the living infant was hers. In response, Solomon asked for a sword and said,

“Cut [Divide—KJV] the living child in two, and give half to one and half to the other!” The real mother spoke up to the king, for her motherly instincts were aroused. She said, “My master, give her the living child! Whatever you do, don’t kill him!” But the other woman said, “Neither one of us will have him! Let them cut him in two!” The king responded, “Give the first woman the living child; don’t kill him. She is the mother.” When all Israel heard about the judicial decision which the king had rendered, they respected the king, for they realized that he possessed supernatural wisdom to make judicial decisions. (1 Kings 3:25-28)

There are several figures of speech that come from this story: A very wise person can be called a Solomon and can be said to have the wisdom of Solomon or the judgment of Solomon. And the phrases cut the baby in half and split the baby are used, such as in court decisions, to say that a wise compromise was made in a difficult disagreement. They can also be used to say that a compromise is impossible, as in “you can’t split the baby.”