1

Part of 1996 Bundeswettbewerb Mathematik

Problems(2)

set of points in space is allowed to mirror a point from the set , image inside

Source: 1996 German Federal - Bundeswettbewerb Mathematik - BWM - Round 2 p1

For a given set of points in space it is allowed to mirror a point from the set with respect to another point from the set, and to include the image in the set. Starting with a set of seven vertices of a cube, is it possible to include the eight vertex in the set after finitely many such steps?

combinatorial geometrygeometrycombinatoricscube

Can a square of side length 5 be covered by three squares of side length 4?

Source: 1996 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1

Can a square of side length

5

be covered by three squares of side length

4

combinatorial geometrycombinatoricsgeometrySquares