Explaining, convincing and proving

Try out this number trick. What happens with different starting numbers? What do you notice?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Try out these calculations. Are you surprised by the results?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Given the products of adjacent cells, can you complete this Sudoku?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

What is the smallest number of answers you need to reveal in order to work out the missing headers?

The Number Jumbler can always work out your chosen symbol. Can you work out how?