Aspire Faculty ID #3714 · Topic: NIMCET 2012 · Just now
NIMCET 2012

What is the maximum number of green roofs?

Solution

Fixed data:

B = Red roof + Black chimney

E = Green roof

Since A and C are adjacent to B, they cannot use Red or Black colour. Therefore, A and C must have White chimney, and their roof can be Green or Yellow.

Case House A House B House C House D House E
1 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Red roof, Black chimney Green roof, White chimney
2 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, White chimney
3 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, Red chimney
4 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, White chimney
5 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, Black chimney
6 Green roof, White chimney Red roof, Black chimney Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney
7 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Red roof, Black chimney Green roof, White chimney
8 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, White chimney
9 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, Red chimney
10 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, White chimney
11 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, Black chimney
12 Yellow roof, White chimney Red roof, Black chimney Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney
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