## Hard puzzles

N points are chosen at random on the cicumference of a circle. A convex n-gon (n sided polygon) is drawn by joining these n points. What is the probability that the center of circle lies inside the region of n-gon?

Solution
Source: a nice senior
Enable Like and Comment

On pressing a button, a random number is generated uniformly between 0 & 1. You keep on generating these numbers until their sum exceeds 1. What is the probability that you need to press the button more than n times? What is the expected number of times you need to press the button?

Hint
Solution

You are initially located at origin in the x-axis. You start a random walk with equal probability of moving left or right one step at a time. What is the probability that you will reach point a before reaching point -b? What is the expected number of steps to reach either a or -b? (a,b are natural numbers)

Solution
Source: Top Quant Interview
Enable Like and Comment

You are taking out candies one by one from a jar that has 10 red candies, 20 blue candies, and 30 green candies in it. What is the probability that there are at least 1 blue candy and 1 green candy left in the jar when you have taken out all the red candies? (Candies of same color are indistinguishable!)

Hint
Solution

An aircraft hovers above sea, trying to catch a submarine moving with a constant velocity under the sea. The submarine is completely invisible, but using a human radar only once, the aircraft knows the exact location of submarine under the sea. The direction of submarine is unknown, but constant. The aircraft can move at twice the speed of submarine. As soon as the aircraft is just vertically above the submarine, Aircrafet can magnetically pick it up. How does the aircraft catch the submarine? How much time ill it take?

PS: This scene is from X-men: First Class. Good x-men are in the aircraft called blackbird, human radar is Banshee, Magnet is Magneto. Bad x-men are in submarine, with Sebastian Shaw is about to cause a war, better catch him soon!

Hint
Solution
Source: Inspired from Rustan Leino's puzzle
Enable Like and Comment

Latest solved Puzzles

Difficulty Level