(written from a Production point of view)
Star Trek 20Q is a handheld electronic game co-released by Mattel and Radica. It is a specialized edition of the base 20Q game invented by Robin Burgener (itself based on the spoken parlor game known as "Twenty Questions"), that began as an experiment in artificial intelligence (AI).
Unlike the regular 20Q game that is shaped like a ball, the Star Trek 20Q unit is shaped like a stylized version of the USS Enterprise seen in the Original Star Trek series. The Saucer is thicker to accommodate the main electronics of the game (mainly the display screen and the control buttons), and the unit fits on a stand shaped like the Star in the TOS-era's Command Division ship's insigniae.
Like "Twenty Questions", the game tries to determine what item (sentient being, place, thing. etc.) in the Star Trek Universe you are thinking of, using as few "Yes or No" questions as possible. The unit asks questions, to which you can reply by pressing the "Yes", "No", "Sometimes" or "Unknown" buttons on the unit, depending on whether the answer to the unit's question is a definite Yes, a definite No, only partially applies to the subject, or you are unsure as to the answer. If the unit can "guess" your item after asking the 20th question, it wins. Otherwise, it will ask 5 more questions and take a second guess, which it still considers a "win" if it's right. If the unit cannot guess your item after the 25th question, it considers you the winner.
The database of information for the game was developed in part by allowing people to play a preliminary version of the game on the official 20Q website. Said database covers information on items from all five TV series and the first ten feature films (as information on the 11th film was not available when the game was produced).