Problem of the Week
A drunk performs a random walk along a street. At one end of the street is a river, and at the other end is a police station. If he gets to either of these ends, he remains there. He starts n steps from the river, and there are N total steps between the river and the police station. What is the prob
Physics
To many, prime numbers are a useless concept studied in maths and soon forgotten about, having no impact on the rest of our lives. While they do have some applications in computing and encryption, primes never seem to crop up in day-to-day life, remaining as “special numbers” that aren’t all that sp
Problem of the Week
There are 25 red balls and 25 blue balls in a bag. Alice and Bob take turns drawing balls from the bag without replacement, with Alice going first. Interestingly, they notice that whenever a red ball was drawn, the next ball drawn (by any person) was never red. Suppose Bob drew m red balls. Given th
Problem of the Week
Hundreds of years ago, scientists believed that air was a pure substance which, alongside earth, wind and fire, made up all matter on Earth. Nowadays, we know that air is a mixture of gases. 1 mole of air contains: 0.78 moles of nitrogen 0.21 moles of oxygen 0.01 moles of argon
Problem of the Week
One of the CCF's guns is designed such that it can launch a projectile of mass 10 kg at a speed of 200 m/s. The gun is placed close to a straight, horizontal railway line and aligned such that the projectile will land further down the line. A small rail car of mass 200 kg travelling at a speed of 10
Problem of the Week
One of the CCF's guns is designed such that it can launch a projectile of mass 10 kg at a speed of 200 m/s. The gun is placed close to a straight, horizontal railway line and aligned such that the projectile will land further down the line. A small rail car of mass 200 kg travelling at a speed of 10