The LogiQuad Game System

The LogiQuad Game System is a 1969 game by John H. Geiger, published by Metroplan.

It is played in a 6x6 board that supports the placement of marbles. These marbles can be placed on top of each other, adding a third dimension to the game.

Players alternate by placing marbles. If a square of 2x2 balls have at least one friendly marble, the player can drop a new marble on top of those four marbles. If the player has three or four of those base marbles, he scores one point. If no move is available, the player must pass. When the entire pyramid is built, wins the player with the highest score.

Geiger, afaict, calls it a game system because he understood that the game material, just like a deck of cards, is a game system. Many different games and puzzles can be designed for it. In the booklet, here are two possible puzzles to play:

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The concept of stacking marbles had other iterations: Upper Hand, aka Pyramids, is a 1985 game by Margalith Akavya, and played on a 5x5 grid,

Each player has 27 marbles, and there is one extra neutral marble (having a third color). The goal is to place all friendly marbles on the pyramid.

• Initially, the neutral marble is placed at the board center. 
• On his turn, a player places a marble on the board. 
• If the placement formed a 2x2 square with three or four friendly marbles, the player moves again. This process continues until no more similar squares are made. 

These rules are very similar to those of LogiQuad's. This could be played in the previous set, which reinforces the game system perspective.

A more modern version of Pyramids is 2018's Mosaic, which uses a bigger 7x7 board.

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Cameron Browne produced another iteration of this idea. He designed Shibumi, a 2011 game system with a 4x4 grid and 16 marbles or three different colors. A book exists with several game rules:

the book is available online

The book gathers games proposed at The Shibumi Challenge where at least 48 games were submitted.
Examples are Spout, a 4x4 version of Upper Hand, and Spoff, a puzzle. 

Browne also designed Margo, a 2006 game, is a 6x6 variant of this same principle; and 2002's Akron, a connection game described at Abstract Games Magazine #14. Both are very good games.