Question

A book having 700 pages his its pages numbered from 1 to 700. If we count all the 3's in the page numbers, how many 3's will be there?
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Answer 1

Answer:

233

Explanation:

pages_700

3,s =233

i,e.234*3

=233

and. (1) page will left

it is not possible to put 3,s in 700 pages

Answer 2

Answer:

141 is the correct answer.

Explanation:

We can solve this problem by considering the different cases for page numbers.

a) The units place is 3:

There are 10 pages that end with 3 in each block of 100 pages (e.g.,$3, 13, 23, ..., 693)$. Since there are 7 such blocks in the book, the total number of pages that end with 3 is $7$×$10 = 70$.

b)The tens place is 3:

There are 10 pages that have a 3 in the tens place in each block of 100 pages (e.g., $30, 31, 32, ..., 39).$ Since there are 7 such blocks in the book, the total number of pages that have a 3 in the tens place is $7$ ×$10 = 70$

c)The hundreds place is 3:

There is only one page that has a 3 in the hundreds place, which is page $300$.

Therefore, the total number of 3's in the page numbers is $70 + 70 + 1 =$$141$

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