Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

I started by wondering ... does the ice cube float at all? Ice isn't that much less dense than water and diamond is a lot more dense than either. Ok, so the puzzle says it does (my subsequent math suggests the diamond is less than ~2.5% of the volume?), but at some point, a bit of the ice melts, and at that point, it's not the diamond that drifts to the bottom of the glass, but an ice cube. As the ice melts, it reduces in size, and so the water level drops. Seeing the answer, this is kind of like assuming a black hole diamond. The black hole diamond would certainly sink whatever ice cub it was in.