Lesson Page numbers on the left and right facing pages of an opened book

Page numbers on the left and right facing pages of an opened book

Problem 1

n + (n+1) = 341


2n = 341 - 1 = 340


n = 340/2 = 170.


ANSWER.  Left page numer is 170;  right page number is 171.

Problem 2

n + (n+1) = 479


2n = 479 - 1 = 478


n = 478/2 = 239.


    Formal answer is 239 for the left page and 240 for the right page.

    But if you open any book, which has traditional numeration, you will NEVER see such pair of pages.

    In traditional numeration, left page has an even number, while the right page has an odd number.

Problem 3

Let x be the smaller number;  then the lerger number is (x+1).


x*(x+1) = 600

x^2 + X - 600 = 0

(X+25)*(X-24) = 0

The roots are 24 and -25, but only positive root x= 24 is meaningful.


ANSWER.  The pages numbers are 24 and 24+1 = 25.


CHECK.  24*25 = 600.    ! Correct !

Problem 4

1) these page numbers are two consecutive integers.


2)  = 75.5 (approximately).


3) Hence the pages are 75 and 76:  75*76 = 5700.


    Formal answer is 75 for the left page and 76 for the right page.

    But if you take a usual book and open it, you will see that an odd page  (with the greater number)  is on the right, 
    while an even page (with the smaller number)  is on the left.

    From this point of view,  the given condition is  WRONG:  you will never see the open book with the numbered pages satisfying the given condition.

Problem 5

Numeration of pages goes from 1.


There are 9 pages with one-digit numbers, from 1 to 9.


There are 90 pages with two-digit numbers, from 10 to 99.


So,  2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.


The rest of numbers are three-digits, and their number is 


     = 611  


So, there are  611  pages with three-digit numbers.


THEREFORE, the total number of pages in the book is  9 + 90 + 611 = 710.      ANSWER