### Novemberish

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.

### Latin Numbers

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

### 2-digit Square

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?

# DOTS Division

##### Age 14 to 16 Challenge Level:

Take any pair of two digit numbers $ab$ and $cd$ where, without loss of generality, $ab> cd$. Form two 4 digit numbers $abcd$ and $cdab$ and calculate: $\frac{abcd^2-cdab^2}{ab^2-cd^2}$ Repeat this with other choices of $ab$ and $cd$. There is a common feature of all the answers. What is it? Why does this occur? Generalise this to $n$ digits for other values of $n$.