Abstract: A three-dimensional logical cube has 6 faces in the same configuration of Rubik's Cube (trademark). A three-dimensional logical cube has an N×N array of cells on each face. Each cell on a three-dimensional logical cube has a numerical value, solid and hollow dots, solid dots, or shapes, on it.

Abstract: An electronic musical page turner is consisted of a LCD (liquid crystal display) display, triple foot actuator switches, and an external personal computer, scanner, USB portable storage device, and USB wireless electronic pen. The system transfers and displays of electronic score music files using many available software and electronic music files format such as PDF, Scorches, Solora, etc . . . The musical score data can be exchanged between the LCD display and a personal computer through the use of foot actuators and command functions on LCD display's control menu. The LCD can display two pages of music score in landscape viewing mode or one page in portrait viewing mode. Foot actuators are manipulated by the performer to progress the sheet music score on the LCD display. The performer can turn the electronic sheet music score to next page, previous page, or home page by pressing specific foot actuator.