Question

Total 1161 digits are used to give numbers to pages of a book. Find how many pages
does the book have.​

Answer 1

ANSWER: 423

DEATAILED EXPLANATION:

From Pages 1 --> 9

We use 9 digits.

Hence 9 Pages [since the digits are singular]

From Pages 10--> 99

We use 2 digits per number.

Therefore Total digits used = 2× 90 =180

Hence 90 Pages.

TILL NOW, WE HAVE USED (180+9) DIGITS TO NUMBER PAGES FROM 1 TO 99.

OR IN OTHER WORDS WE CAN SAY THAT WE HAVE NUMBERED 99 PAGES WITHOUT REACHING THE DESIRED DIGIT COUNT (1161).

From Pages 100 --->999

We use 3 digits per number.

Therefore, total digits used = 3 × 900(Because 900 numbers lie between 100 and 999 when we include '100' in the counting)

Total digits used = 2700

Hence 900 pages.

BUT, WE REQUIRE ONLY 1161 DIGITS. SO WE KNOW THAT THE REQUIRED NUMBER OF PAGES LIES BETWEEN 99 AND 900.

99< No. of Pages< 900

Now, we are sure that there are atleast 99 pages in the book. We also know that if we start adding pages after the 99th page, we will enter 3-digit number's category, i.e 100 then 101 then 102....

When this happens we use 3 digits per number.

LETS SUPPOSE WE USE 'n' 3 DIGIT NUMBERS [THEN BY THIS WE ALSO MEAN THAT WE NUMBER n PAGES WTH 3 DIGIT NUMBERS.] THEN NO. OF DIGITS USED WILL BE 3n.

BUT WE HAVE ALREADY USED 189 DIGITS.

AND REQUIRED NO. OF DIGITS = 1161

THEREFORE, 3n+ 189 = 1161

=>3n = 972

=> n= 324

So the total no. of pages = 324 + 99= 423