Solutions

Solution to the coconut problem

Well, the solution is not even n-nary. It goes something like this :-
a) Go to the eight floor and drop the coconut.

b)If it breaks
{ then the floor "x" is such that 1 <= x <= 8.
So start from 1st floor and drop...2nd floor and drop....8th floor...
Until you get x.
}

c)If it doesnt go to 8+7 = 15th floor.Drop from here.
If it breaks
{then the floor "x" is such that 8 <= x <= 15.
So start from 8th floor and drop...9th floor and drop....15th floor...
Until you get x.
}

d)If it doesnt go to 8+7+6 = 21st floor.Now the search for x is between
15 and 21.

:
:
It goes on till 8+7+6+5+4+3+2+1 = 36.

Solution to the Prison Problem

Richie got a beautiful deduction as :-
Prime numbered cells will be closed.
The state of the composite numbered cells depends on the number of its unique factors.

Among composite numbers , consider the numbers which are squares. e.g. 1 , 4, 9 , 16 ...These have an ODD number of factors. eg :- take 49. The factors of 49 are 1,7,49. So Door# 49 will be opened during 1, closed during 7 and re-opened during 49. So, All the numbers which are perfect squares will be opened and the rest will be closed.

Note:-

There are some more puzzles coming. But yesterday's coffee discussion was centered around the fact that Kannada movie heroes are ugly. I couldnt disagree on the fact that, the movie which was being showed on TV at the cafeteria when this discussion was going on, was a lesser know movie called "Chaitrada Premanjali".On second thoughts,should heroes always be good-looking ?