WorldQuant interview questions

Some sample questions: Q. You have a biased coin in which the probability of getting a head is 51%. Create an event out of this coin which has a probability of 25%. Q. There is a calculator in which all digits (0 to 9) and the basic arithmetic operators (+, -, *, /) are disabled. However other scientific functions are operational like exp, log, sin, cos, arc tan, etc. The calculator currently displays a 0. Convert this first to 2 and then to 3. Q. There are five points in an equilateral triangle of side length 1. Prove that there are two points with distance less than 1/2.