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Part of 2010 Portugal MO
Problems(2)
Bones and Candles - Portuguese MO, Problem 1, 2010
Source:
8/28/2010
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.
combinatorics proposedcombinatorics
Numbers on a pentagon - Portuguese MO, Problem 4, 2010
Source:
8/28/2010
Giraldo wrote five distinct natural numbers on the vertices of a pentagon. And next he wrote on each side of the pentagon the least common multiple of the numbers written of the two vertices who were on that side and noticed that the five numbers written on the sides were equal. What is the smallest number Giraldo could have written on the sides?
least common multiplenumber theory proposednumber theory