Odd and even numbers

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Can you put the numbers in the correct place in this Carroll diagram?

In this game the winner is the first to make the total 37. Is this a fair game?

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?

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Are these games fair? How can you tell?