Finding Centre of the Mass of a Ruler

We are trying a fun way to find the centre of the mass of a ruler. If you hold your index fingers in front of you, put a ruler on top of them and start moving your hands towards each other, your fingers end up right at the unique point where the ruler's mass is centred. We added weight on one side to make it more challenging, and then we tried moving fingers at different speeds and placing fingers at the asymmetrical position. But every time we fingers meet right under the centre of the mass of the ruler. How does it work? The finger that is closer to the centre of the mass carries more weight and friction increases letting the other finger come closer. Then the same thing is happening with the second finger, which allows the first finger to slide.