A hot air balloon uses a gas flame to heat the air it contains to a temperature required to enable it to hover at a small distance above ground level. The mass of the balloon, ropes, basket, and riders is 240 kg and the volume of the balloon is 1100 m³. The temperature of the surrounding air is 15°C

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

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

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

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

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

There are 100 lockers that line the main hallway of Holyport. Every morning, the security guards make sure that all of the lockers are closed so that there will be an orderly start to the day. One day, 100 mischievous students decide that they will play a prank. The students all meet after school en

Alan and Claire live by the old Scottish saying, “Never have whisky without water, nor water without whisky!” So one day, when Alan has in front of him a glass of whisky, and Claire has in front of her a same-sized glass of water, Alan takes a spoonful of his whisky and puts it in Claire’s water. Cl

The evening after national lockdown was lifted, a couple decided to celebrate their newfound freedom at a bar down the street. Much to their surprise, they find four other couples there who had the same idea. Eager for social contact, every person in the five couples enthusiastically hugs each perso

You want to create a family tree, but you are having trouble tracking down your grandmother’s birthdate. The only clue you found was a letter written from your great grandfather to your great grandmother on the day you grandmother was born. Unfortunately, some of the characters were smudged out, rep

Problem of the week: 18 March 2023 This week's question is one from the 2023 edition of the Chemistry Race, and is a particularly satisfying one to solve, without being too difficult! Thermogravimetric analysis (TGA) is an analytical method for investigating temperature-dependent phase transitions and chemical reactions of

Problem of the week: 29 January 2023 Five line segments of length 2, 2, 2, 1 and 3 connect two corners of a square as shown in the diagram. What is the shaded area?