How many pages? (1)

Number Theory Level 2

3401 3401 digits are used to print the page numbers of a book.

How many pages does the book have?

Try How many pages? (2)


The answer is 1127.

Ethan Mandelez by Ethan Mandelez , 15, Malaysia

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3 solutions

Ethan Mandelez
May 6, 2020

We can list them strategically:

Page 1 - 9 ---> 9 digits

Page 10 - 99 ---> 99 - 10 + 1 = 90 pages 

                   : 90 x 2 = 180 digits

Page 100 - 999 ---> 999 - 100 + 1 = 900 pages 

                       : 900 x 3 = 2700 digits

9 + 180 + 2700 = 2889 digits so far,

3401 - 2889 = 512 digits for 4 - digit page numbers

512 4 \frac{512}{4} = 128

Total number of pages ---> 999 + 128 = 1127 pages

2 Helpful 0 Interesting 2 Brilliant 0 Confused
Trupal Panchal
May 6, 2020

9 (1 digits) = 9 digits
90 (2 digits) = 180 digits 900(3 digits)=2700 digits

total 2889 digits are used and 3401-2889=512 digit left to use, now on all numbers came in 4 digits so 512/4= 128 pages can be printed .

so in total 9+90+900+128=1127 pages are printed.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Zakir Husain
May 17, 2020

Answer from Python

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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