There are 2019 coins on a table. Some are placed with head up and others tail up. A group of 2019 persons perform the following operations: the first person chooses any one coin and then turns it over, the second person choses any two coins and turns them over and so on and the 2019-th person turns over all the coins. Prove that no matter which sides the coins are up initially, the 2019 persons can come up with a procedure for turning the coins such that all the coins have smae side up at the end of the operations. indian olympiadgraphcombinatoricsTST