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# A textbook has pages. How many of the pages have page numbers whose digits add up to exactly ​?

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A textbook has $$1000$$ pages. How many of the pages have page numbers whose digits add up to exactly $$4$$?

Feb 14, 2023

#1
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If the textbook has 1000 pages, then the page numbers range from 1 to 1000. To find the number of pages with page numbers whose digits add up to exactly 4, we can use the following formula:

Number of pages = $\sum_{i=1}^{9}$(Number of pages with i as the last digit)

For example, the number of pages with 0 as the last digit is the same as the number of pages with 4 as the last digit, as both digits add up to 4. Similarly, the number of pages with 1 as the last digit is the same as the number of pages with 3 as the last digit, as both digits add up to 4.

Using this formula, we can calculate that the number of pages with page numbers whose digits add up to exactly 4 is 12.

Feb 14, 2023
#2
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1 == 4
2 == 13
3 == 22
4 == 31
5 == 40
6 == 103
7 == 112
8 == 121
9 == 130
10 == 202
11 == 211
12 == 220
13 == 301
14 == 310
15 == 400

Feb 14, 2023