Given that you can cut a pizza n times, what is the maximum number of pieces you can obtain?

There are 100 people who will shake hands with each other. Is it possible to make the number of times people shaking hands all different?

You have a 3 and a 5 litres water container with no measurement markings. How can you use the containers to make 4 litres of water?

How would you prove that the square root of 3 is irrational?

There are 30 people in one room. What is the probability that exactly 2 of them have the same birthday?

Do there exist 2 integers, x and y such that x^2 + y^2 = 1 000 003?

There are 10 boxes with full of coins – 9 of the boxes contain real coins and 1 box contains fake coins. Given that real coins weigh 10g, and fake coins weigh 9g, how many times would you have to measure their weights to work out which box contains fake coins?

**Answers/Explanations**

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