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Thank you for your solutions to this problem. You found several different ways of tackling it.
Fergus, Nathan, Samuel and Jesse from Rutherglen Primary School drew another hundred square with the numbers on the opposite side of a printed hundred square. Jesse says:On the back of $100$ was $91$, on the back of $58$ was $53$, on the back of $23$ was $28$ and on the back of $19$ was $12$.
Mikey from Archbishop of York CE Junior School wrote:Having printed the page out I realised that if you turned it over you could see through the page. Looking where $100, 58, 23, 19$ would be meant you could read off the answers as $91, 53, 28, 12$. Or is this cheating?
I don't think this is cheating at all Mikey! Mikey then realised something else which was also spotted by "N" (he or she didn't give us a full first name):If you draw a mirror line down the middle of the square you will be able to work out what number will be behind each number. You choose a number, then find its mirror on the other side of the line, this 'mirror' number will be the number on the reverse!
This is also a very handy method - well noticed. "N" sent an image with the "mirror line" drawn in:
Well done to George from Bradon Forest, Mary from St Swithun's, Miss Grewcock's Class from St James CEVA Primary and Joshua from Queen Victoria Primary who also noticed this mirror line.
Devonshire Maths Club, Devonshire Primary School have found a pattern which they describe:
Very well noticed. Luke from Queen Victoria Primary found another way:
Jake from the same school as Luke explained this a bit more generally:
Sohpie and Anna from St Swithun's and Gabrielle from Hayesfield Girls School also tackled the problem in this way.