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by shashank.ism » Mon Feb 15, 2010 11:09 pm
Four circles having radius 1 cm, 2 cm, 3 cm and 4 cm intersect each other to create maximum possible number of bounded regions. What is the minimum possible number of different colours required to fill in the bounded regions so that no two adjacent regions are filled with the same colour?

A) 5
B) 4
C) 3
D) 6
E) 7
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by komal » Mon Feb 15, 2010 11:24 pm
shashank.ism wrote:Four circles having radius 1 cm, 2 cm, 3 cm and 4 cm intersect each other to create maximum possible number of bounded regions. What is the minimum possible number of different colours required to fill in the bounded regions so that no two adjacent regions are filled with the same colour?

A) 5
B) 4
C) 3
D) 6
E) 7
If there are 2 circles then 3 colors are required
3 circles 4 colors
4 circles 5 colors

Therefore for 4 circles the minimum number of different colors required to fill in the bounded regions so that no two adjacent regions are filled with same color is 5. Hence (A) is correct .
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by harsh.champ » Thu Feb 18, 2010 4:43 am
komal wrote:
shashank.ism wrote:Four circles having radius 1 cm, 2 cm, 3 cm and 4 cm intersect each other to create maximum possible number of bounded regions. What is the minimum possible number of different colours required to fill in the bounded regions so that no two adjacent regions are filled with the same colour?

A) 5
B) 4
C) 3
D) 6
E) 7
If there are 2 circles then 3 colors are required
3 circles 4 colors
4 circles 5 colors

Therefore for 4 circles the minimum number of different colors required to fill in the bounded regions so that no two adjacent regions are filled with same color is 5. Hence (A) is correct .
Hey komal ,
My answer would [spoiler]be C(3)[/spoiler].It is written that no two adjacent regions should have the same color.
So, we can use 2 colors(suppose red and black)twice in an alternating pattern.
I guess you made a mistake of taking all the colors to be different.

Note:-The pattern would be like a square(the square vertices being the centre of the 4 circles.
Also,only 2 circles will intersect at a time.(We will not get a 3 set intersection ,only 2 set intersections)
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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