My head-canon is that Solomon had, like, ten trials lined up for the baby case but the one woman failed so hard on the first one that he ended up with a whole free-ass day, just... Calendar cleared.

"We'll cut the baby in half and... What? You said what? Wow. I... Okay. You know what? There was going to be a whole philosophical journey I was going to take you on here, comparing and contrasting property and people, responsibility to ownership, culminating with recognition of the mystery of soul and the supremacy of G~d in all things, but... No! I don't care who the biological mother is. Give the baby to the woman who *doesn't think it's okay to cut babies in half!* Case closed praise YHWH!"