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Problem #3:
for pages 1-9 there are 9 digits
for 10 through 19 there are 20 digits. Proof:
10 (2 digits)
11 (2 digits)
12 (2 digits)
13 (2 digits)
14 (2 digits)
15 (2 digits)
16 (2 digits)
17 (2 digits)
18 (2 digits)
19 (2 digits)
2+2+2+2+2+2+2+2+2+2=20
Following the same logic, from 10-99 there are 180 digits, because 90x2=180.
So far you have 9 digits plus 180 digits. 189 digits.
From 100-199 you have 300 digits.
That's 300 digits plus 189 digits, 489 digits.
200-999 is 2400 digits, because 300x8=2400
2400 digits plus 489 digits gives you 2889 digits.
Your goal is to hit 2901. So from 1-999, you have 2889 digits so far.
You need another 12 digits to hit 2901, because 2901-2889=12.
1000=4 digits
1001=4 digits
1002=4 digits
4x3=12 digits
Your final answer should be: 1002 pages.
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