Book Wrecker
You are holding a book, which has 500 non-blank pages individually labelled.
If you tear off all the pages starting from the one labelled 'page 311' until the one labelled 'page 458', this book will have 350 non-blank pages left.
Now, if you tear off all the pages from the one labelled 'page 216' until the one labelled 'page 242', how many non-blank pages will be left?
Note: One sheet of paper has 2 pages, one page on one side and one page on the other. The first labelled non-blank page is on top of all the other non-blank pages. All non-blank pages are labelled sequentially with no blanks in between.
This is one part of 1+1 is not = to 3 .
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1 solution
If you tear off all the pages starting from page 311 until page 458, you expect that the total number of pages lost is 4 5 8 − 3 1 1 + 1 = 1 4 8 . However, the actual number of non-blank pages left is 350, meaning it lost 5 0 0 − 3 5 0 = 1 5 0 pages.
Wait a minute, it lost an extra 2 pages! Where did the extra 2 pages come from?!
You have to realize that, first, one sheet of paper has two pages, if you tear this sheet, both pages on both sides will be lost.
Second, due to the structure of books and because all non-blank pages are labelled sequentially with no blanks in between, if you flip open a book, either:
(1) Odd pages are always on the left and even pages always on the right
or
(2) Even pages are always on the left and odd pages always on the right
Hence, in order for the book to lose 2 extra pages, it must be the case that pages 310 and 459 are torn together with pages 311 till 458, and since 311 is an odd page and 458 is an even page, we conclude that (1) must be the case for this book.
Therefore, if you tear off the pages from 216 until 242, you expect that the number of pages torn is 2 4 2 − 2 1 6 + 1 = 2 7 . However, since page 242 is an even page and is on the right side, when torn, the page at the back will also be lost, so the number of pages lost is actually 28. 3 5 0 − 2 8 = 3 2 2 , there are 322 non-blank pages left.