M4maths Previous Puzzles

26 Jun 2009 Orange Puzzle (Friday Again)

4 oranges are distributed among 4 friends named as Ankur, Parag, Milan and Deepak.
There are certain conditions for the distribution.
* If Ankur receives 1 orange then it is necessary to give 1-1 orange to all others.
* Parag has disagreed to receive 3 oranges.
* If Parag obtains 2 oranges then Ankur does not receive any orange.
* If Milan gets 3 oranges then Deepak gets 1 orange necessarily.
* Only Deepak can take all the 4 oranges.
How many methods are possible for the distribution of oranges?

OPtion

1) 35,
2) 16,
3) 12,
4) 22,
5) 25,
6) 19,
7) 27,
8) 20,
9) 21,
10) 30,

Solution

Category and no. of methods in each category are given in the table below

Category No. of methods in the category
4 orange to one person 4
3 to one and 1 to other 12
2-2 oranges 6
2 to one and 1-1 to other two persons 12
1-1 to four persons 1
Now according to condition 1, If Ankur receives 1 orange then it is necessary to give
1-1 orange to all others,
Therefore out of 10 methods in which Ankur receives 1 orange only that 1 is correct
in which all
boys get 1-1 oranges.
According to condition 2, Parag has disagreed to receive 3 oranges,
Therefore out of 3 methods in
which Parag gets 3 oranges, 2 are rejected. (One method has been rejected in the
previous condition)
According to condition 3, If Parag obtains 2 oranges then Ankur does not receive any orange,
Therefore out of 6 methods in which Parag receives 2 oranges only 3 are correct.
In remaining 3 methods
2 are rejected in first condition hence 1 method is rejected in this step.
According to condition 4, If Milan gets 3 oranges then Deepak gets 1 orange necessarily
Therefore out of 3 methods in which Milan gets 3 oranges only 1 method is correct.
Out of other 2 methods 1 is rejected. (Other 1 has been rejected in first condition)
According to condition 5, Only Deepak can take all the 4 oranges.
Therefore out of 4 methods
as given in the table above, 3 are rejected
Total no. of rejected methods is 9+2+1+1+3=16

Correct Option: 6 Best Solution (0)