5
Part of 1997 May Olympiad
Problems(2)
areas of a hexagon with all angles equal and sides 1,2,3,4,5,6
Source: III May Olympiad (Olimpiada de Mayo) 1997 L2 P5
9/17/2022
What are the possible areas of a hexagon with all angles equal and sides , and , in some order?
geometryhexagonareas
43 friends fror birthday, cake of 15-gon
Source: III May Olympiad (Olimpiada de Mayo) 1997 L1 P5
9/17/2022
When Pablo turns , he throws a party inviting friends. He presents them with a cake n the form of a regular -sided polygon and on it candles. The candles are arranged so that between candles and vertices there are never three aligned (any three candles are not aligned, nor are any two candles with a vertex of the polygon, nor are any two vertices of the polygon with a candle). Then Pablo divides the cake into triangular pieces, by means of cuts that join candles to each other or candles and vertices, but also do not intersect with others already made. Why, by doing this, Paul was able to distribute a piece to each of his guests but he was left without eating?
combinatoricscombinatorial geometry