Question

We publish a monthly magazine of 84 pages. Once I found that in a magazine 4 pages were missing. One out of them was page number 29 it is known that the page number of the last page of the magazine is 84, (including the cover pages), The numbers printed on the missing pages were :

• A. 29, 52, 53
• B. 30, 55, 56
• C. 28, 52, 53
• D. Cannot be determined

Answer 1

The correct option is B 30, 55, 56

The middlemost pages of the magazine are shown in the figure numbered 42 and 43.
Did you notice that the front pages on the left side of the magazine (as shown in figure) are divisible by 2 and the odd numbers are on the back side of these numbers? Note that I am talking about the left side of the magazine when it is open as shown in figure.

So the missing page numbers with 29 will be 30 and the corresponding number on the right side will be 51 and 52.

Alternatively: Since the magazine has 84 pages it means there are 21 sheets of paper, which are folded in middle. Now see the pattern of page numbers:
$\begin{array}{cccc}Leftside& Rightside& & \\ 1,2& 83,84& & \\ 3,4& 81,82& & \\ 5,6& 79,80& & \\ 7,8& 77,78& & \\ 9,10& 75,76& & \\ ⋮& ⋮& ⋮& ⋮\\ 29,30& 55,56& & \\ ⋮& ⋮& ⋮& ⋮\\ 41,42& 43,44& & \end{array}$

Thus we can say that the sum of the page numbers on a sheet on one side is always 85. Hence the page numbers printed on the sheet of paper is 29, 30 and 55, 56.