Question 115
Sharon has a chandelier containing $n$ identical candles. She lights up the candles for $n$ consecutive Sundays in the following manner: the first Sunday, she lights up one candle for one hour; the second Sunday, she lights up two candles, conveniently chosen, for one hour; and continues in the same fashion, increasing the number of candles lighted each Sunday by one, until in the $n$th Sunday, she lights up all the $n$ candles for one hour. For what values of $n$ is it possible for all the $n$ candles to be of equal lengths right after the $n$th Sunday?