Can You Solve this Ice Diamond Riddle? ft. Vsauce’s Michael Stevens

I think the water level goes down. Since however much the ice is melted doesn't matter to the water level too much, we can shift our perspective to think about what happens when the diamond is inside the ice cube and when it's outside the ice cube. When the diamond is inside the ice cube, the diamond adds more weight to the ice, which forces the ice cube down into the water a little more, and thus displaces more water, so the water level has to be high in the initial state. And thinking about the other case, where the diamond is not present in the ice, obviously there's no extra weight added to the ice, and it therefore it doesn't displace as much water, so the water level must be lower.