MathDB

a) The vertex

A_1

of the regular

12

-gon (dodecagon)

A_1A_2...A_{12}

is marked with "

-

" and all the rest

--

with "

+

". You are allowed to change the sign simultaneously in the

6

vertices in succession. Prove that is impossible to obtain dodecagon with

A_2

marked with "

-

" and the rest of the vertices

--

with "

+

".
b) Prove the same statement if it is allowed to change the signs not in six, but in four vertices in succession.
c) Prove the same statement if it is allowed to change the signs in three vertices in succession.

Problem Statement