Coins on a table
Source: Indian TST 2019 Practise test Day 2 P3
August 11, 2019
indian olympiadgraphcombinatoricsTST
Problem Statement
There are coins on a table. Some are placed with head up and others tail up. A group of 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 -th person turns over all the coins. Prove that no matter which sides the coins are up initially, the 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.