Series - I

1, 4, 4, 8, 32, 40, 1280, ....

Theory of Countability

Consider a uniform distribution between 0 and 1. Let us randomly pick up a number between 0 and 1, say X
a) What is the probability that X = 0.5?
b) What is the probability that X is rational?
c) What is the probability that X is irrational?

Descending down a building

You need to descend down a 200m building but you only have a 150m long rope. There is a hinge present at  the top and also at the 100m level of the building. How will you descend down?

6 Colored balls

We have two red, two green and two yellow balls. For each color, one ball is heavy and the other is light. All heavy balls weigh the same. All light balls weigh the same. How many weighing on a beam balance are necessary to identify the three heavy balls?

Hole and the Board

Cut this board into only 2 pieces so that they fit into the given hole.