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Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

Where should you start, if you want to finish back where you started?

How many six digit numbers are there which DO NOT contain a 5?

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Can you produce convincing arguments that a selection of statements about numbers are true?

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

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?