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).