MathDB

In the vertexes of a regular

31

-gon there are written the numbers from

1

31

, ordered increasingly, clockwise oriented. We are allowed to perform an operation which consists in taking any three vertexes, namely the ones who have written

a

b

, and

c

and change them into

c

, a\minus{}\frac{1}{10} and b\plus{}\frac{1}{10} respectively (

a

becomes

c

b

becomes a\minus{}\frac{1}{10} and

c

turns into b\plus{}\frac{1}{10} Prove that after applying several operations we can reach the state in which the numbers in the vertexes are the numbers from

1

31

, ordered increasingly,anti-clockwise oriented.

Problem Statement