Eleksius, the dual of twenty questions
Everybody knows the game 20 questions where you think of one object and people ask 20 yes or no questions to figure out what the object is. Few years ago I invented a dual version of the game called Eleksius where you think of a yes or no question and people ask you if an arbitrary object has the property. (It was motivated by the card game Eleusis quoted from Empire of the Ants by Werber.) Interestingly, Eleksius is significantly more difficult than 20Q, usually hundreds of objects has to be presented in order to get the right answer. The two games are symmetric in the sense that each round (asking a binary question or presenting an object) eliminates the possible targets from the set of all possible targets (objects or binary questions, respectively). Thus the optimal strategy is to choose the one that would cut all possible targets in half which guarantees maximal information gain for both. However, somehow the 20Q is easier than Eleksius. Why?
- At least 2 players are needed. One plays “the god” and the others are “the people” who worship and wants to know what the god is thinking.
- The god thinks of a simple binary question about an arbitrary object such as “Is X edible?” or “Is X not edible?”.
- At the beginning, the god gives two objects with corresponding yes/no answers.
- The people takes turn to ask the god about objects of their choice, the god answers.
- When one of the people thinks that he/she knows the answer they declare to be a “prophet”.
- When a prophet is declared, everybody asks to the prophet instead of the god and the prophet answers yes or no. If the god does not agree with the answer the prophet is fired. The god can also test the prophet by sending him/her objects.
- When the god thinks the prophet has the answer, the prophet reveals the answer, and the god confirms. If the prophet is right, the game ends.
- Use a question that is clear and objective. Subjective questions like “Do I like X?” is a not allowed.
- Use a question that sufficiently many objects correspond to each answer yes and no.
Variation I (2009.06.18.)
- You can declare to be a god of a category. This is desirable when your property is well defined within such category. It also makes the game a little easier.
- For example, you can start with “I am a god of animal kingdom. Rat has it, but elephant doesn’t.”
This game can be generalized into hand gestures, body pose, tales, and often becomes a trick question rather than an inductive puzzle.