MathDB

2

Part of 2020 Bundeswettbewerb Mathematik

Problems(2)

Moving a knight in the minimal number of moves

Source: Bundeswettbewerb Mathematik 2020, Round 1 - Problem 2

11/17/2020
Konstantin moves a knight on a n×nn \times n- chess board from the lower left corner to the lower right corner with the minimal number of moves.
Then Isabelle takes the knight and moves it from the lower left corner to the upper right corner with the minimal number of moves.
For which values of nn do they need the same number of moves?
combinatoricscombinatorics proposedchess boardChess knight
No rational solutions to a system of equations

Source: Bundeswettbewerb Mathematik 2020, Round 2 - Problem 2

11/17/2020
Prove that there are no rational numbers x,y,zx,y,z with x+y+z=0x+y+z=0 and x2+y2+z2=100x^2+y^2+z^2=100.
number theorynumber theory unsolvedrational numberalgebrasystem of equations