Hundred Square

On the back of 100 is 99 On the back of 58 is 53 On the back of 23 is 28 On the back of 19 is 12

Patterns: Both numbers in the pair usually have the same tens digit apart from 100/99 and 1/10 Units digit of sum of pairs is always 1

Thank you for your solutions to this problem. You found several different ways of tackling it.

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 Christian 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:

100 square with mirror line drawn in

Devonshire Maths Club, Devonshire Primary School have found a pattern which they describe:

The tens in each pair don't change ie $58 - 53$, both $5$ tens.

The units in each pair add up to $11$.

$100$ & $91$ are different. $100$ has a nought in the tens column, and $90$ has a nine. In the units, $1 + 0$ doesn't = $11$.

$100 = 9$ tens & $10$ units. $91 = 9$ tens & $1$ unit. Now the tens stay the same, and the units add up to $11$.

Very well noticed. Well done!