Question 157
When Paulo turned 15, he invited 43 friends to a party. The cake had the shape of a regular polygon with 15 sides and there were 15 candles on it. The candles were placed in such a way that no three candles were in a straight line. Paulo divided the cake into triangular pieces where each cut joined two candles or joined a candle to a vertex. Moreover, no cut crossed another one already made. Explain why, by doing this, Paulo was able to give a piece of cake to each of his guests, but he himself was left without any.