Bones and Candles - Portuguese MO, Problem 1, 2010
Source:
August 28, 2010
combinatorics proposedcombinatorics
Problem Statement
There are several candles of the same size on the Chapel of Bones. On the first day a candle is lit for a hour. On the second day two candles are lit for a hour, on the third day three candles are lit for a hour, and successively, until the last day, when all the candles are lit for a hour. On the end of that day, all the candles were completely consumed. Find all the possibilities for the number of candles.