MathDB

1

Part of 1978 Bundeswettbewerb Mathematik

Problems(2)

Bundeswettbewerb Mathematik 1978 Problem 1.1

Source: Bundeswettbewerb Mathematik 1978 Round 1

10/12/2022
A knight is modified so that it moves pp fields horizontally or vertically and qq fields in the perpendicular direction. It is placed on an infinite chessboard. If the knight returns to the initial field after nn moves, show that nn must be even.
combinatoricsChessboardknightEven
Bundeswettbewerb Mathematik 1978 Problem 2.1

Source: Bundeswettbewerb Mathematik 1978 Round 2

10/12/2022
Let a,b,ca, b, c be sides of a triangle. Prove that 13≤a2+b2+c2(a+b+c)2<12\frac{1}{3} \leq \frac{a^2 +b^2 +c^2 }{(a+b+c)^2 } < \frac{1}{2} and show that 12\frac{1}{2} cannot be replaced with a smaller number.
inequalitiesTrianglealgebra