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

It goes down. Since the ice cube floats, the initial displacement of the water in the cup is equal to the weight of the ice in the cube plus the diamond i.e. the weight of the ice in the ice cube plus the volume of the diamond * density of the diamond. When the cube melts the volume of water displaced is now the volume of water due to the melted ice cube plus the volume of the diamond. The volume of water due to the melted ice cube is equal to the original weight of the ice in the ice cube and since the density of the diamond is greater than 1 it floating contributes more to the initial displacement than when it sinks. Just one thing to add; If the ice cube initially sank, because the diamond was large enough, the water level would still go down once the ice cube has melted, because water expands when it freezes.