Copyright (c) Gigamic Games

Each player has 12 stones. The game is played on the following board.

GOAL - Wins the player with the longest chain of his own stones.
MOVE - On each turn, each player can: 
Remove one empty cell - each player can only do this six times.
Drop a stone into an empty cell
The two cells below the chosen cell (either to remove or drop a stone) must not be empty (i.e., were removed or already have stones).
An example

In this game, Black has won, since Black's longest chain has 7 stones, and White's has only 4 stones.

David Glaude has a website with more information about Zenix.