MathDB

2

Part of 2016 Bundeswettbewerb Mathematik

Problems(2)

Geometric game: Maximizing area

Source: Germany 2016 - BWM Round 1, #2

11/12/2016
A triangle ABCABC with area 11 is given. Anja and Bernd are playing the following game: Anja chooses a point XX on side BCBC. Then Bernd chooses a point YY on side CACA und at last Anja chooses a point ZZ on side ABAB. Also, X,YX,Y and ZZ cannot be a vertex of triangle ABCABC. Anja wants to maximize the area of triangle XYZXYZ and Bernd wants to minimize that area. What is the area of triangle XYZXYZ at the end of the game, if both play optimally?
geometrygeometry unsolvedarea of a triangleareaGame Theory
Sum of Triangular Number and Prime Number

Source: Bundeswettbewerb Mathematik 2016, Round 2 - #2

9/7/2016
Prove that there are infinitely many positive integers that cannot be expressed as the sum of a triangular number and a prime number.
number theoryprime numbersinfinitely many solutions