Multiple choice

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 of the following is true?

  1. At least two houses have black chimney.

  2. At least two houses have red roofs.

  3. At least two houses have white chimneys

  4. At least two houses have green roofs

  5. At least two houses have yellow roofs
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

House B has a red roof and black chimney. House E has a green roof, so its chimney must be white (can't be red because that would match a roof color, and can't be black because B uses black and adjacent houses can't share colors). Working backwards: House D's roof can't be green (E uses green), can't be red (B uses red), so D's roof is yellow, making D's chimney white. House C's roof can't be yellow or green (D and E use them), so C's roof is red, making C's chimney white. So at least houses C and D have white chimneys.

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