You might have heard various variations of this problem before.

You have 2 ostrich eggs in your hand (fairly hard shells) and you are in front of a 50 story building. The basic challenge is to figure out which is the floor from and above which the eggs will break on impact to the ground when you drop them from a window of that floor. Of course, this can be done with only one egg. You start with first floor – if it does not break, go to second floor. And keep doing this till you find the floor where it does break. The minimum number of tries you will need to guarantee finding out that floor is 50. (Basically, in the worst case, you have to keep trying all the way to the top)

But you have 2 eggs. Now, the challenge is to find out the minimum number of tries with which you can guarantee finding out that threshold floor at or above which an egg will break (one try means one dropping of an egg). Needless to say, once an egg breaks, you cannot use it again.

In a remote part of an African jungle once lived a bunch of lions. No other animal ever came there. Except one day, somehow a deer showed up. Of course, the lions immediately wanted to eat it. Now, these lions were very smart and very courteous. Some might even say they took special “pride” in it 🙂

Puns aside, here are the rules of the puzzle:
(*) the lions have an understanding that only one lion – whoever is first to touch – can kill and eat a deer. (when one attacks, nobody else does; that is where the courteous bit comes in)
(*) they also know that this deer has a property that whichever lion attacks and eats it, itself becomes a deer the next day (which can be attacked and killed by other lions then)
(*) Every lion is desperate to eat a deer. They are okay to live the rest of their life as a deer itself – but will not do so if they know they might get killed the next day by the lions.

Question: Will the deer survive?

Two students independently come to the library every day after dinner between 7pm and 9pm. Each stays for exactly one hour and then leaves. At any night, what is the probability that they met? (meaning that both were in the library at the same time even if for a very short while)