a game of coloring edges of graph I have a clique of size 5 which is partially colored(black or white). I have to color remaining edges so that each of the triangle  has either 1 or 3 black edges. How should I go about coloring the graph or how can I tell this is not possible. 

Hint: Given a (complete) coloring of the clique, each vertex of the form $v_{i} v_{i+2}$ is uniquely determined.
It then remains to check that triangles of the form $v_i , v_{i+2}, v_{i+4} $ satisfy the conditions.

Hint: Assume that such a coloring is possible. Label the black edges $-1$ and the white edges $1$. Then, we know that the product each triangle is $-1$. Use this to get conditions on the edges.
