In 1956 Robert Abbott invented a game he called Eleusis. In 1959 Martin Gardner popularized the game in his Scientific American column. Eleusis is what's called an "induction game" which means that players need to try to induce the rules of the game. Inductive games are compared to deductive games, where players know what the rules are and try to deduce their moves. Yes, I find the terms confusing but, nonetheless, they're worth knowing because if you find yourself enjoying Eleusis you'll know how to refer to that type of game.
Eleusis is played with an ordinary deck of cards. The idea of the game is that one player creates a secret rule and other players have to play cards that satisfy that rule. Ultimately, of course, the goal is to determine what the rule is.
Before you set out to find instructions for Eleusis, Abbott recommends a simplified version of the game created by another man, John Golden, and named "Eleusis Express". Its instructions are on this page.
Eleusis Express needs at least three players since, at any given time, one player holds the secret rule and isn't playing cards. So, think of Eleusis as a fun family or party game, although having more than eight players participate is not recommended in the instructions.
Eleusis Express is a great game for teaching pattern matching, which is an absolutely critical skill in solving mathematical problems. I like this about the game. If you find yourself liking these induction games you might enjoy this web page which discusses some induction games. Wikipedia has articles about a few inductive games as well: Mao, Penultima, and Zendo. A Gamut of Games, by Sid Sackson, includes one induction game, Patterns II. A list of games included in the book is in this Wikipedia article. Copies of the book are available at Amazon.com.