Question

A note book is made up of sheets folded in the middle and stapled. Each sheet forms two leaves ie, four pages. On removing some papers of the first-half and second-half of the book, Joe found the number of the leaves in the first case as odd and in the second case as even. If the sum of the numbers of the pages on the last leaf of the book is 63, then what could be the maximum possible sum of the numbers on the pages of leaves that were left in the book?

Answer 1

Hey mate!

Here is your answer

Last 2 pages are 31 and 32 ----> 31 + 32 = 63

In 1st half of book (pages 1-16) Joe removed an odd number of leaves

In 2nd half of book (pages 17-32) Joe removed an even number of leaves

The minimum number of leaves Joe could have removed is 3:

1 from the 1st half of the book

2 from the 2nd half of the book

The minimum possible sum of the numbers on the pages he removed is:

(1+2) + (17+18) + (19+20) = 77

The maximum possible sum of the numbers on the pages that were left in the book is

(1 + 2 + 3 + ... + 32) − 77 = (32)(33)/2 − 77 = 451

Hope it helps ☺️!

Have a great day !