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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.

##### Age 11 to 14Challenge Level

Choose any four digits (from 0, 1, 2, ... , 9) and place them in the cells below (you can repeat digits). Then add these two totals together.

For example: Try a few examples of your own.

Is there a quick way to tell if the total is going to be even or odd?

Can you make a total of 200?
How many ways are there of doing this?

If we use four 0s, the total would be 0.
If we use four 9s, the total would be 396.
Which numbers between 0 and 396 is it possible to make?

With thanks to Don Steward, whose ideas formed the basis of this problem.