MathDB

At each vertex of a

13

-sided polygon we write one of the numbers

1,2,3,…, 12,13

, without repeating. Then, on each side of the polygon we write the difference of the numbers of the vertices of its ends (the largest minus the smallest). For example, if two consecutive vertices of the polygon have the numbers

2

and

11

, the number

9

is written on the side they determine. a) Is it possible to number the vertices of the polygon so that only the numbers

3, 4

and

5

are written on the sides? b) Is it possible to number the vertices of the polygon so that only the numbers

3, 4

and

6

are written on the sides?

Problem Statement