Directions: Five houses lettered A,B,C,D, & E are built in a row next to each other. The houses are lined up in the order A,B,C,D, & E. Each of the five houses has a colored chimney. The roof and chimney of each house must be painted as follows. i. The roof must be painted either green, red ,or yellow. ii. The chimney must be painted either white, black, or red. iii. No house may have the same color chimney as the color of roof. iv. No house may use any of the same colors that the every next house uses. v. House E has a green roof. vi. House B has a red roof and a black chimney Which must be false?

Option B claims House A and C have different color chimneys. From our analysis in the previous question, both House C and House D have white chimneys. House A's chimney could also be white (it's adjacent to B, which has black). So it's possible for A and C to both have white chimneys, making the statement false. Let's verify: If A has white chimney and green roof, B has red roof and black chimney, C has red roof and white chimney, D has yellow roof and white chimney, E has green roof and white chimney. This satisfies all constraints, and A and C have the same chimney color (white). So option B must be false.