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Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

### N000ughty Thoughts

How many noughts are at the end of these giant numbers?

### 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}.

##### Age 11 to 16Challenge Level

To help you get started on this very challenging problem, Alison made a series of videos showing some ways to work on this problem. Perhaps after watching each video you could have another go at solving the problem for yourself before looking to see what Alison does next.

In this video, Alison outlines the problem and starts thinking how to get started.

In this video, Alison multiplies and divides to try to get close to the solution.

In this video, Alison restates the problem in a different way.

In this video, Alison thinks about factors.

In this video, Alison finds a representation that helps.

In this video, Alison considers the units digit.

In the final video, Alison tries some more combinations and finds one that works!