5
Part of 2019 May Olympiad
Problems(2)
max triangles from regular n-gon May Olympiad (Olimpiada de Mayo) 2019 L2 P5
Source:
9/24/2021
We consider the vertices of a regular polygon with sides. There is a set of triangles with vertices at these points with the property that for each triangle in the set, the sides of at least one are not the side of any other triangle in the set. What is the largest amount of triangles that can have the set?[hide=original wording]Consideramos los n vértices de un polígono regular de n lados. Se tiene un conjunto de triángulos con vértices en estos n puntos con la propiedad que para cada triángulo del conjunto, al menos uno
de sus lados no es lado de ningún otro triángulo del conjunto. ¿Cuál es la mayor cantidad de triángulos que puede tener el conjunto?
combinatorial geometrycombinatoricsregular polygon
Can $Ana$ complete the second row so that $Beto$ does not achieve his goal?
Source: May Olimpiad 2019 Level 1 P5
3/9/2021
There is a board with three rows and columns. In the first row are written the numbers integers from to inclusive, ordered from smallest to largest. In the second row, writes those same numbers but ordered at your choice. In each box in the third row write the difference between the two numbers already written in the same column (the largest minus the smallest). have to paint some numbers in the third row so that the sum of the numbers painted is equal to the sum of the numbers in that row that were left unpainted. Can complete the second row so that does not achieve his goal?
combinatorics