Being curious

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Can you work out the probability of winning the Mathsland National Lottery?

Which numbers can we write as a sum of square numbers?

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

What is special about the difference between squares of numbers adjacent to multiples of three?

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

There are unexpected discoveries to be made about square numbers...

Can you create a Latin Square from multiples of a six digit number?

A 2-digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?