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Robert from Matthew Pearce Public School sent a solution to the first part of this problem. Robert says:

put $3, 9, 5, 7, 1$ in odd numbers and less than ten
put $2, 4, 6, 8$ in even numbers and less than ten
put $17, 11, 13, 15, 19$ in odd numbers and not less than ten
put $10, 12, 14, 16, 18$ in even numbers and not less then ten

So, the completed Carroll diagram would look like this:

first solution

Well done also to Eliza from Danebank School who also completed this diagram.

Rowena from Christ Church Primary told us how she went about filling in the second Carroll diagram:

I decided the numbers that were between $10$ and $20$ did not include $10$ or $20$, this left $11-19$, all these numbers have an odd tens digit so they went in the bottom left corner. All the remaining numbers must be in the 'Not between $10$ and $20$' column, $10$ and $30$ have odd tens digit so they went at the bottom of that column, all the $20$'s went in the top. I decided that $0$ is an even number, so $1-9$ have even tens digit.

Here is a picture of Rowena's completed diagram:

second diagram

You've explained this very well, Rowena. It's interesting that you've decided that the numbers $1-9$ have zero as their tens digit and that zero is even. Perhaps some of you have comments about this?