them Notice that moving any coin and flipping it decreases the difference in the number of heads by 1 If you move a head and flip it, you decrease the number of heads on the table with the coins by 1, but you do not increase the number of heads on the table without coins (because it becomes a tail) If you move a tail and flip it, you do not change the number of heads on the table with coins, but you increase the number of heads on the table without coins by 1 Therefore by moving 30 coins and flipping them, the tables will have the same number of heads