What is the ruling on this game, and is it permissible according to Sharia?

This method of studying knowledge, encouraging its learning, and solidifying it is legitimate and desirable for students of knowledge, as it involves testing quick wit and recalling evidence. The Prophet, peace and blessings be upon him, used to encourage his companions to learn knowledge through various means, and perhaps he would pose riddles to them and test their faculties, such as in the hadith: "Indeed, among trees, there is a tree whose leaves do not fall... it is the date palm." In this, there is an examination by the scholar of the students' minds, and an incitement to understanding in knowledge.