2 · Six people, and no way out

Six people, two colors, and every string clickable. The triangle count can never reach zero.

Try this. Chase the count downward. The article's tests walk all 32768 colorings: none is safe, and the luckiest contain exactly two one-color triangles. See if you can find one of those.

Only the first offending triangle is thickened, so the picture stays readable while you work.