Coin Tossing Experiment

Consider a coin tossing experiment. Let X be the number of heads if you toss a coin for 99 times. Let Y be the number of heads if you toss a coin for 100 times. What is the probability that X is less than Y?

Prime Numbers

How many prime numbers exist between 2 consecutive prime numbers?

House with too many doors

Have a look at the house plan at the right hand side, with five rooms and sixteen doors in total. The intention is to make a run through the rooms and pass each of the sixteen doors exactly once.

How many ways can it be done?

Color the Cube

Given the cube and 2 colors such that each color is on exactly 3 faces, how many different coloring combinations are possible?

Taxi Service

Mr. Kothari runs a taxi service in Ahmedabad. Every day, he travels from Ahmedabad to one nearby city and back. All the cities are less than 100 km away from Ahmedabad. Everyday morning, Mr. Kothari fills his car’s fuel tank to the brim. On a full tank, the car can travel maximum 250 km. Unfortunately, Mr. Kothari forgot to fill his tank today. What is the probability that he will run out of fuel during the day?

Maximize the product

Using the digits 1 up to 9, two numbers must be made. The product of these two numbers should be as large as possible. All digits must be used exactly once.
What are these 2 numbers?

Hole and the Board - 3

A carpet of size 10 by 10 meters should be placed in a room of size 12 by 9 meters. In the center of the room, there is an aquarium of size 8 by 1 meters (see the figure below). The carpet should be cut into no more than two pieces (i.e. one cut in total).

Four Fruits

In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly.

How many of them guessed three fruits correctly?

Subtraction

How many times one can subtract 2 from 32?

Hole and the Board - 2

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

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.