### DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

### 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?

# What a Joke

##### Stage: 4 Challenge Level:

Each letter represents a different positive digit

$$\frac {AHHAAH}{JOKE}= HA$$

What are the values of each of the letters?