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A book has 400 pages numbered 1,2,3 and so on. How many times does the digit 3 appear in the page numbers?

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Ques. A book has 400 pages numbered 1,2,3 and so on. How many times does the digit 3 appear in the page numbers?

Solution:

Let us calculate several 3 in the first 99 pages.

1 3s in the first 9 pages.

1 3s in the pages from 10 – 19.

1 3s in the pages from 20 – 29.

11 3s in the pages from 30- 39 (one each for 30- 32 and 34- 39 and 2 for 33).

6 3s in the pages from 40- 99 ( 43, 53, 63, 73, 83, 93).

So, we have 20  3s in the first 99 pages.

Now,

We have 20 3s on pages 100- 199, 20 3s on pages 200-299, and 0 3s on page 400.

Now, 

For pages, 300-399, there are 100 3s for the hundred digit in addition to the 20 3s found in the tens and ones digit.

Conclusion: 

So, we have a total of 20 + 20 + 20 + 120 = 180  3 appearing in the page numbers.


Last Updated : 15 Mar, 2024
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