A child's construction set contains virtual intelligence, is interactive and smart, characteristics that may be exhibited to a player during player construction activity with the set and, thereafter, during continuing play and instills a sense of unpredictability to play. The set incorporates a programmed controller (17), a speaker (23), special ("smart") play pieces or blocks (1,3,5,7, et cet.) and a base (15) on which to position the play pieces or blocks. Sensors (A1-C3), referred to as "hot spots", are distributed at various positions about the base and are coupled to the controller, whereby the controller identifies special play pieces and the location of those play pieces when the respective play piece is installed at one of those positions. Some of the special play pieces may depict characters, some contain electrically operated devices, and some contain a player operated input device. The controller issues speech messages or other audible effects through the speaker to effect a virtual personality to the character play pieces; controls operation of electrically operated devices in special blocks, and detects and responds to player inputs from the player input blocks. Through wireless communication devices, the controller may acquire information from and supply speech messages to accessory blocks that are used off the base of the construction set.