Question 665207: A book has 500 pages numbered 1, 2, 3, and so on. How many times does the digit 1 appear in the page numbers?
Answer by kevwill(135)   (Show Source):
You can put this solution on YOUR website! In the first 99 pages there are:
1 one in the first 9 pages,
11 ones in pages 10-19 (one each for 10 and 12-19, and two for 11)
8 ones in pages 20-99 (21, 31, 41, 51, 61, 71, 81, and 91)
So we have 20 ones in the first 99 pages.
Likewise we have 20 ones in pages 200-299, 20 ones in pages 300-399, and 20 ones in pages 400-499. There are 0 ones on page 500.
For pages 100-199, there are 100 ones for the hundreds digits in addition to the 20 ones found in the tens and ones digits.
So we have a total of 20 + 120 + 20 + 20 + 20 = 200 ones on the page numbers.
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