A Problem with Typical Statement.
A notebook is made up of sheets folded in the middle and stapled. Each sheet forms two leaves i.e. four pages. On removing some papers of the first half and second half of the book, Calvin Lin 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
, then what could be the maximum possible sum of the numbers on the pages of the leaves that were left in the book.
This problem is a tribute to Calvin Lin sir.
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We know that the two last pages are 31 and 32 since their sum is 63. So the pages in the first half of the book are 1-16, and the second half 17-32.
He removed odd number of leaves in the first half (1 - smallest) and even number in second half (2-smallest). To maximize the sum of whats left, he should be removing pages 1&2 from first half and pages 17,18,19 &20 from second half.
Total number of pages is (1+32)(16) = 528. Subtract the pages that were removed. 528 - (1+2+17+18+19+20) = 4 5 1