Solve this Problem?

Question

A building has 100 floors. You are given 2 glass balls.
A ball breaks when dropped from a particular floor and any floors above that.
What is the minimum number of trials you would need to drop the ball to find the exact floor from which the ball breaks?

Answer 1

Hi there, I've just faced this question in my pre-interview preparatory test. Well frnd, I'm letting u know it's answer.

The answer is 14. The strategy is to drop the first ball from the K-th story; if it breaks, you know that the answer is between 1 and K and you have to use at most K-1 drops to find it out, thus K drops will be used. It the first ball does not break when dropped from the K-th floor, you drop it again from the (K+K-1)-th floor, then, if it breaks, you find the critical floor between K+1 and K+K-1 in K-2 drops, i.e., again, the total number of drops is K. Continue until you get above the top floor or you drop the first ball K times. Therefore, you have to choose K so that the total number of floors covered in K steps, which is K(k+1)/2, is greater that 100 (the total size of the building). 13*14/2=91 -- too small. 14*15/2=105 -- enough.
Obviously, the only possible strategy is to drop the first ball with some "large" intervals and then drop the last ball with interval 1 inside the "large" interval set by the two last drops of the first ball. If you claim that you can finish in 13 drops, you cannot drop the first ball for the first time from a floor above 13, since then you won't be able to detect the critical floor 13. The next cannot be above 25 etc.

Answer 2

Alrite, lets say the floor that it breaks at is X. First you drop a ball from the 10th floor. If it doesn't break, then the 20th, then the 30th, then the 40th...The floor that is a multiple of 10 that the first ball breaks at is called Y. Once you find Y, then drop the second ball from Y-9 (you already tried Y-10), Y-8,Y-7, and stop a Y-1(you already tried Y-0), or until you find X. And you've found it. The most amount of tests you would have to do is 19, and thats if the breaking point is floor 100.

Answer 3

The problem is poorly stated, as you might pick a simply random strategy and get lucky, in which case you will find the exact floor on the 2nd trial (you picked it right the first time, and tried one floor below to confirm the hypothesis, and the 2nd ball didn't break).

...assuming this is a math class and not a logic class...

This is more complex than it may at first seem. You have two basic approaches; start on the first floor and then skip by 3s after that (1, 4, 7, ...) which could take you as many as 33 tries if the answer is 100.

Another strategy is to start on floor 50 (or 51). If the ball breaks, you start over on the first floor and skip by 2. If it doesn't, you try floor 75, etc. This strategy would set you at worst case 26 trials (better than the first strategy), and if you kept getting lucky, you would zero in in 6 trials.

Answer 4

The number of trails will be dictated by when the glass ball brakes. It depends on the strength of the glass ball to with stand the impact of the falling balls.

One approach is to go to the 50th floor, and drop one ball out of the window. If it brakes, then the required height is less then the 50th floor. You could start at the 1st floor and work your way up one by one until the second glass ball brakes.

If the first glass ball does not brake after it's drops from the 50th floor, you could go to the 60th floor and drop it form there. If it brakes at the 60th floor, then go up in ones from the 50th floor using the second glass ball, until that one brakes.

If the first glass ball does not brake at the 60th floor, then try going up to the 70th floor.
Repeat the procedure.

If you have the manufactures data list displaying the force of impact the glass can withstand, you could calculate the distance and hence know the height it could be dropped from. So two drops could confirm your answer.

Answer 5

A glass ball will break on the first trial, even if it is dropped from the 1st floor.

Answer 6

Fx is particular floor if we drop balls it will break

in order to make trial we need to try from the lowest floor.
since there are 2 balls so minimum trial is

floor umber x/2

if limit break is fllor 25
so minimum trial is 25/2=12.5
since there no partialnumber for trial it should be 13

the formula became

ntrial=round(xfloor/2)

Answer 7

1, the lowest floor from which a ball can be dropped is the first, so if it breaks there, it is the only trial you need.

Answer 8

9

Answer 9

49