Problems – We Solve Problems
Filter Problems
Showing 1 to 12 of 12 entries

Auxiliary simialr triangles , Extremal principle (other) , Pigeonhole principle (area and volume)

A unit square is divided into $n$ triangles. Prove that one of the triangles can be used to completely cover a square with side length $\frac{1}{n}$.

Isometry helps solve the problem , Pigeonhole principle (area and volume) , Point symmetry

On the planet Tau Ceti, the landmass takes up more than half the surface area. Prove that the Tau Cetians can drill a hole through the centre of their planet that connects land to land.

Area inequalities , Partitions into pairs and groups bijections , Pigeonhole principle (area and volume)

In a square which has sides of length 1 there are 100 figures, the total area of which sums to more than 99. Prove that in the square there is a point which belongs to all of these figures.

Geometry on grid paper , Pigeonhole principle (area and volume) , Various dissection problems

One corner square was cut from a chessboard. What is the smallest number of equal triangles that can be cut into this shape?

Packing problems , Pigeonhole principle (area and volume) , Systems of points

Prove that, in a circle of radius 10, you cannot place 400 points so that the distance between each two points is greater than 1.

My Problem Set reset
No Problems selected