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Binary Search on a plane & in a cube

In the plane x and y are integers that range from 0 to 128. There are 16,641 points in this plane. In the cube x, y and z are integers that range from 0 to 128. There are 2,146,689 points in this cube. The applet will choose a mystery point. You should be able to find the point in no more than 6 tries. This is true in both the plane and the cube! Why?