Answer
Try it and see. Your fingers will meet at the 50-cm mark.
Work Step by Step
If one finger happens to be farther from the center, it supports less of the meterstick, and the lower normal force means less friction. That finger slides under the meterstick, getting closer to the center, while the other finger tends to stick to the meterstick.
The process brings both fingers to more symmetrical positions, and at the end, they meet in the middle.
