Problems – We Solve Problem
Filter Problems
Showing 1 to 2 of 2 entries

#### A segment inside the triangle is smaller than the largest side , Hexagons , Pigeonhole principle (angles and lengths) , Regular polygons

There are 7 points placed inside a regular hexagon of side length 1 unit. Prove that among the points there are two which are less than 1 unit apart.

#### Equilateral triangle , Hexagons , Pigeonhole principle (finite number of poits, lines etc.) , Polygons and polyhedra with vertices in lattice points , Regular polygons

A regular hexagon with sides of length 5 is divided by straight lines, that are parallel to its sides, to form regular triangles with sides of length 1 $($see the figure$)$.

We call the vertices of all such triangles, nodes. It is known that more than half of the nodes are marked. Prove that there are five marked nodes lying on one circumference.

My Problem Set reset
No Problems selected