Fair experiment with unfair coin!

The puzzle is simple to state: You are given a biased coin with 60% chance for getting heads and 40% chance of getting tails while tossing. Design an experiment with two equally likely outcomes using the coin.

Think out of the box!

2 rooms, 1 light bulb in one room and the other room has 3 switches out of which only one of the light bulb switches on/off. The rooms are not viewable from each other. You as a single person has just one chance to find which switch operates the bulb. How can this be done?

An Interval Graph

Six professors had been to the library on the day when the rare tractate was stolen. Each had entered once, stayed for some time and then left. If two were in the library at the same time, then at least one of them saw the other. Detectives questioned the professors and gathered the following testimony:


A said he saw B and E
B reported he saw A and I
C claimed he saw D and I
D said he saw A and I
E testified to seeing B and C
I said that she saw C and E

One of the professors lied. Who was it?

Unit distance coloring

Imagine that each point on the plane takes a color. What is the minimum number of colors needed to color all the points so that any two points which are at distance exactly 1 unit get two different colors?

The Plane in the Wind

An airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It traverses with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less, or the same if, throughout both flights, at the same engine speed, a costant wind blows from A to B?