What is the ruling on mathematical puzzles, and is it permissible to use them in competitions and gatherings?

There are types of riddles: recommended, forbidden, and permissible. The recommended type is that which is related to Islamic knowledge, used to exercise the mind and stimulate competition, such as the riddle "The tree whose leaves do not fall" (the date palm), which the Messenger of Allah, peace and blessings be upon him, posed. The forbidden riddle is that which mocks the essence of Allah, or His Messenger, or the religion, such as saying, "I have on earth what Allah does not have in heaven," which is forbidden and suggests a false meaning. As for the permissible riddle, it is that which pertains to mathematical, cultural, or political matters, provided that they are not excessive, free from gambling, and not accompanied by insults or curses.