Aspire Faculty ID #16470 · Topic: NIMCET 2009 · Just now
NIMCET 2009

Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each house must be painted as follows:

The roof must be painted either green, red, or yellow.
The chimney must be painted either white, black, or red.
No house may have the same colour chimney as the colour of roof.
No house may use any of the same colours that the every next house uses.
House E has a green roof.
House B has a red roof and a black chimney.
What is maximum total number of green roofs for houses?

Solution

E already has a green roof.
Adjacent houses cannot use any colour that the next house uses, so D cannot have a green roof (because E has green).
B already has a red roof, so only A and C are free to possibly take green roofs.

We can choose roofs:
A – green, B – red, C – green, D – yellow, E – green

This satisfies all rules and gives 3 green roofs (A, C, E).
We cannot make B or D green, so more than 3 green roofs is impossible.
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