Why do this problem?
would make a good starter for those children who are working on the writing and ordering the numbers from $1$ to $20$, and might be suitable for use in conjunction with a number line.
You could display a number line and ask the group to count outloud along it with you. You could then show them a number line just numbered up to $5$, as in the picture. Encourage the children to count along this number line, filling in the blanks as they go.
Then, introduce the problem orally and ask learners to work in pairs on the challenge, with their own number line to help. It may be necessary to clarify the meaning of 'digit' if the children are not familiar with this term.
What do we mean by 'digit'?
Which is the tenth digit? How do you know?
Pose similar questions for the children, such as "If Lee wrote all the numbers from $1$ to $20$, how many digits would she have written altogether?" "How many sevens has Lee written? What digit did she write after each of these sevens?"
Children could be encouraged to count carefully along a number line.