There are $$1991$$ white balls and $$1000$$ black balls of the same size in Bag A. Ming simply takes 2 balls from Bag A and put them outside. If two of the balls are of the same colour, Ming will take out one Black ball from Bag B and it back to Bag A. If two of the balls are of the different colour, Ming will put the white colour ball back to Bag A.  Question: How many balls are left in Bag A after Ming takes $$2989$$ balls out from Bag A? What color are they? 
Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers