Writing Digits

Lucy and Alice from Stoke By Nayland Middle School sent us their work. They explained their answer very clearly.

We wrote the numbers in consecutive orders from 1 to 20 on a piece of paper.

We then counted to the 17th digit. This happened to be the number 3 out of the number "13". (If you count the 17th digit from the number line below, you will see that it is the number 3, not the 1st 3!) So the last
number she wrote was 13.

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1 2 3 4 5 6 7 8 9 10 11 12 13 14
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Then Lucy and Alice went on to think about how they might apply this method to another similar problem.

For example, if you were given this problem below, using our solution above you could quickly work out the answer. Lee was writing all the counting numbers from 1 to 100. She stopped for a rest after writing eleven digits. What was the last number she wrote? Using our solution, I found the answer to be the 0 from the number "10".