MathDB

We consider a number of points in a plane. Each of these points is connected to at least one of the other points by a line segment, in such a way that a figure arises that does not break up into different parts (that is, from any point along drawn line segments we can reach any other point).. We assign a point the ”order”

n

, when in this point

n

line segments meet. We characterize the obtained figure by writing down the order of each of its points one after the other. For example, a hexagon is characterized by the combination

\{2,2,2,2,2,2\}

and a star with six rays by

\{6,1,1,1,1,1,1\}

. (a) Sketch a figure' belonging to the combination

\{4,3,3,3,3\}

. (b) Give the combinations of all possible figures, of which the sum of the order numbers is equal to

6

. (c) Prove that every such combination contains an even number of odd numbers.

Problem Statement