Challenge Level

Choose any four digits (from 0, 1, 2, ... , 9) and place them in the cells below (you can repeat digits).

Read the two 2-digit numbers across and add them together.

Read the two 2-digit numbers down and add them too.

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.*