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ujjagrawal

Member Since 24 May 2012
Offline Last Active May 15 2013 06:22 AM
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Topics I've Started

An Uncertain Meeting

16 August 2012 - 08:59 AM

There are two friends, who decide to meet at a place between 5 PM to 6 PM everyday. What are the chances that, on a given day, they will be able to meet. Provided-
Attached File  friends.jpg   9.83KB   80 downloads

Case 1: They agreed whoever comes first, will wait for 15 minutes for another friend to arrive.
Case 2: One friend wait for 10 minutes and other for 20 minutes for another friend to arrive.

And which of the above two cases holds better chances of there meeting ?

Elevators problem

31 July 2012 - 10:35 AM

Most of the people, I understand, must not be happy with the logic by which the elevators on their building works. This is an opportunity for you to work on a logic that should be efficient, fair and a practical one.

There is a 12 floors building (excluding ground level) with 2 elevators. Can you work out what should be the ideal position for the two elevators (in terms of floor numbers), while they are not in use i.e. idle. Assume equal probability of getting calls from all 12 floors.

An unfair coin

27 July 2012 - 10:30 AM

An unfair coin has the property that when flipped four times, it has the same probability of turning up 2 heads and 2 tails (in any order) as 3 heads and 1 tail (in any order). What is the probability of getting a head in any one flip?

A merciless emperor

26 July 2012 - 09:26 AM

There's a merciless emperor who has 500 bottles of very expensive wine in his cellar.

An assassin infiltrates the wine cellar to poison the wine. Fortunately the emperor’s guards catch the plotter after she has poisoned only one bottle. Unfortunately, the guards don’t know which one of the bottles is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

The emperor decides he will get some of the prisoners in his dungeons to test the wine as he has handful of them about to be executed.

What is the smallest number of prisoners that must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

Classic eggs problem

09 July 2012 - 11:47 AM

You have been given three eggs and your job is to figure out how high an egg can fall from a 120 story building before it breaks. The eggs might break from the first floor, or might even survive a drop from the 120th floor, you have no prior information about it. Except all three eggs are know to be of exactly same strength.

What's the most efficient way to drop the eggs i.e. reducing the number of times you need to drop eggs and still able to determine the answer? You are allowed to break all three eggs, as long as you identify the correct floor afterwards.

After you've solved the above problem, generalize. Define the "break floor" as the lowest floor in a building from which an egg would break if dropped. given an n story building and a supply of m eggs, find the strategy which minimizes (in the worst case) the number of experimental drops required to determine the break floor.