Humpty-Dumpty and the Game

Problem Statement Humpty and Dumpty are very close friends. Humpty has recently performed exceptionally well in the End semester exams, so he has gained a lot of confidence. He challenges Dumpty for a Nim game. But Dumpty, as we all know, completely outwitting him, challenges him for a unique game of its own kind. Humpty settles after the argument that they will use following function somewhere i