The problems we want you to solve are below.
Two different integers between 1 and 10 are chosen at random. What is the probability that they are consecutive?
There is a group of n students. Each one will make up a 4 character word out of a made-up alphabet which has only 10 characters in total. Grecia will bet with Holly that if there are 3 students whose words are anagrams of each other then Grecia will give 1 gold coin to Holly, and otherwise Holly will give 1 gold coin to Grecia. What is the smallest size of n for which it becomes good for Holly to bet?
You and your friend live in a grid-like city. Every edge of the grid is a road. The distance from your place to your friend's place is n roads north and m roads east. You and your friend decide to visit each other but both of you leave at the same time and walk at the same speed. If both of you take 'optimal paths' (minimising the length of the paths), what's the probability that you will meet on your way?