If you never played this game, even in its most basic version (a demo disk released for free), the basic goal was to collect certain cubes while avoiding being shoved off the edge by the darker grey or black cubes rolling towards you. In earlier versions of this game (released in Japan and Australia that I've found an emulator for online and will provide later), the graphics were 2D and overhead, whereas in the release for Playstation the graphics were 3D and featured the player as a human character running inside of the puzzles.
There were 3 different types of cubes that were present in this game: normal cubes, which were a grey color and were meant to be cleared; forbidden cubes, which were black and should be avoided and allowed to roll off the edge of the map; and advantage cubes, the light green ones that should be collected in order to reap, well, advantages. Cubes could be caught by tapping the X button on your Playstation controller to place an "X" on the map, and then tapping it again to collect the cube once it had rolled over it. If you failed to get this cubes, or were crushed as they rolled forward the player character would be stunned for a few seconds and the game would advance over them. This usually made you restart back from the beginning of the level, of which there were 10.
While all of this sounds pretty boring considering the awesome new games, I appreciated I.Q. for the fact that it combined a number of fairly different gaming mechanics to make this a pretty difficult game to beat. Along with the different types of cubes to either avoid or capture (avoiding the black cubes exploded a whole line of oncoming cubes), different rows of cubes would move faster or slower than others, some levels included multiple layers of cubes, and there were different characters that could be gained through achievements that would run faster than the original character you were given. Similarly, if you played exceptionally well, you would get perfection scores, which would add additional rows of space to the map—super helpful in some of the more complex puzzles later in the game.