Problems 1721–1730

Q1729 We have \(n\) coins, all placed heads up on a table. It is permitted to select any \(k\) of the coins and flip them; and to do a similar operation repeatedly. Here, \(k\) is a fixed positive integer less than \(n\). The aim is to get all of the coins facing tails up. Prove that this can be done if and only if either \(n\) is even or \(k\) is odd.