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 that the 33rd ball drawn was red, what is the sum of all possible values of m?....
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....
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....
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....
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....
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....
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....
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....
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....
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!....