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## 'Writing Digits' printed from http://nrich.maths.org/

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".