Let n be a positive integer. there are n lamps each with a switch that changes the lamp from on to off, or from off to on, each time it is pressed . the lamps are initially all off. you are going to press the switches in a series of rounds. in first round you are going to press exactly 1 switch in the second round you are going to press exactly 2 switches and so on so that in the Kth round you are going to press exactly k switches. in each round you will press each switch at most once. your goal is to finish a round with all of the lamps switches on.

determine for which n you can achieve this goal.