BRAIN TEASER:

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 very next house uses.
v.      House E has a green roof.
vi.     House B has a red roof and a black chimney

1.        Which of the following must be true ?

a)      At least two houses have black chimney.
b)      At least two houses have red roofs.
c)      At least two houses have white chimneys
d)      At least two houses have green roofs

e)      No two houses have same coloured chimneys

2.        Which must be false ?

a)      House A has a yellow roof
b)      House A & C have different color chimney
c)      House D has a black chimney
d)      House E has a white chimney

e)      None of these

3.        If house C has a yellow roof. Which must be true.

a)      House D has a white roof                                                 

b)      House E has a black chimney
c)      House E has a red chimney                                 

d)      House D has a red chimney

e)      House E has a white chimney