The Textbook of Number Theory

The first 9 pages each contribute 1 digit, but then the pages 10 to 99 have 2 digits, and the pages 100 to 999 have 3 digits.

So we can write a formula...

Digits in book = N if N<9

Digits in book = 2N-9 if 10<N<99

Digits in book = 3N-99-9 if 100<N<999

3N-108= 2832

N= 980.

Note---(At 100 pages, the book has 191 digits, and at 999 pages, the book would have 2889, so we know the answer is somewhere from 100 to 999.)

From 1 to 9 all no have 1digit . From 10 to 99 all no have 2 digits .

So from 1to 99 the total no of digits are [1×9+2×90]=189

The book has 2832 digits .So all the rest pages have 3 or 4 digit no or so on.

The left digits are (2832-189)=2643.

So the book has 3 digit no (2643÷3)=881

So there is no pages of 4digit no. as the total no of 3 digit no. is 900.

In this book the 3 digited paper is 881 that is<900.

So the total no of pages are (881+99)=980.

that's 2832 - (189) = 2643 2643/3 = 881 881+99 = 890