Ice Diamond Riddle SOLUTION ft. Vsauce's Michael Stevens

I understood nothing. 
If water level = 0, adding the ice should increase the level, then it's 0 + A.
When ice melts, and the diamond sinks, you add their volumes, so water level will increase again. It'd be 0 + B
  
B is the total volume of melted ice + volume of the diamond
A is a fraction of the volume of ice + diamond that's filling the space since it's floating, so it should be less than the total volume of the ice when it melts. I know water has more volume when it's between 0 and 4ªC, but still, it shouldn't be greater than B unless it's totally sinking


So what am I missing here? Shouldn't the water level increase after the ice melts?