Question 66
Integers are written at the vertices of an $n$-gon, $n\ge3$. Each vertex number has the same parity as the sum at its two neighbors: an even number has an even neighboring sum, and an odd number has an odd neighboring sum. Which statement must be true?
(A)There are more even than odd numbers.
(B)There are more odd than even numbers.
(C)The number of vertices bearing odd numbers is even.
(D)$n$ is a multiple of 3.
(E)None of the above.
(A)There are more even than odd numbers.
(B)There are more odd than even numbers.
(C)The number of vertices bearing odd numbers is even.
(D)$n$ is a multiple of 3.
(E)None of the above.