**"Hard"**

## Dice game – 7 or 12?

*By admin On April 8, 2012 · 5 Comments*

Two people, ‘A’ and ‘B’ play a game of dice. 2 dices are continuously being thrown on the table. ‘A’ wins if 12 shows up, ‘B’ wins if two 7′s come up in consecutive throws. Game ends whenever there is a winner. What is the probability that ‘A’ wins?

## Find the subsets

*By admin On April 6, 2012 · 2 Comments*

You are given a set of ‘n’ unique numbers. What is the maximum number of subsets that you can form such that if any two random subsets is chosen, they have exactly one element in common?

## Crazy man in the airplane!

*By admin On February 2, 2010 · 2 Comments*

A line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let’s say that the nth passenger in line has a ticket for the seat number n.)

Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random.

What is the probability that the last (100th) person to board the plane will sit in his proper seat (#100)?

## Lake Monster

*By admin On January 31, 2010 · 2 Comments*

You are on a rowboat in the middle of a large, perfectly circular lake. On the perimeter of the lake is a monster who wants to eat you, but fortunately, he can’t swim. He can run (along the perimeter) exactly 4x as fast as you can row, and he will always run towards the closest bit of shore to your boat. If two paths take him to this location equally quickly, he will arbitrarily choose one. If you can touch shore even for a second without the monster already being upon you, you can escape. The monster can reverse direction instantaneously and you can turn your boat instantaneously. Suggest a strategy that will allow you to escape, and prove that it works.

7 thieves wanted to lock the treasure looted from a ship. They wanted to put N no. of locks to the treasure where each lock had multiple keys. Find the minimum number of locks N and minimum no. of keys K with every thief subject to the following conditions:-

All the locks should open each time a majority of thieves(4 or more) try to open the locks.

At least one lock remains unopened if less than 4 thieves try opening them.

All locks should have same no. of keys.

All thieves must have same no. of keys with them.

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