Logic - truth and lies in a circular table.

Question

Germans lie when talking about Americans, and Americans lie when talking about Germans. Germans tell the truth when talking about Germans, and Americans tell the truth when talking about Americans.

Now $n$ people sat at a circular table, from Germany and America. All $n$ people say to their right handed neighbor that "your right handed neighbor is about to lie to his right handed neighbor." What can we deduce about $n$, and the arrangement of Germans and Americans?

I got $n$ is a multiple of $4$, but can't find the arrangement of Germans and Americans.

Answer 1

• informations about n : multiple of 8

• informations about arrangements: cycles of "xyxyxyxy" where "x x x x " and " y y y y" are either:

  1- S S N N

  or

  2- S N N S

where N are "not same" to S and the last one is "same nationality" as S.

• proof:

Lets assume x1 told truth , which means x3 has same nationality to x1 which means x5's nationality differs which means x7 is same to x5 which means x9=x(8+1) differs from x7 and same to x1.

If we rather assume that x1 lies, means x3's nationality is different,x5=x3 and x7=x1 and the cyclic x9 is x1.

Note that the arrangement of "x1 x3 x5 x7" is independant to "x2 x4 x6 x8"

Any different value of n can expose the cyclic logical arrangement to be flawed.