A circle is divided into 6 sections, in each of them is written a number from 1 to 6 clock-wise. You are able to add 1 to any two numbers that are near each other. Is it possible to get all the numbers equal?

Question

welshfella · Answer

I wonder - Does the question imply  that ALL the numbers 1 to 6 are written in the circle?

zyberg · Answer

Yes.

welshfella · Answer

Any ideas? I'm afraid I haven't!

zyberg · Answer

I have got no ideas as well ;/ 
It is from a theme of even and odd numbers. So it got to do something with that, but I have no idea how it would work in this case!

mathstudent55 · Answer

Now what do you do?
|dw:1465911108504:dw|

zyberg · Answer

Well, I know how to draw a circle. ;)

zyberg · Answer

Solved it! 
If anybody were to be interested: to get everything equal to 6 you need to add 15, however, at one time you can add only 2. How about making everything equal to 7? 15 + 6 = 21 the same thing. 
To generalize:
to make all pieces equal to 6 + n you would need to add 15 + 6n numbers, however, since 15 + 6n is odd (even + odd = odd) and you can add only even number (2) it is not possible!