Turn, turn, turn: The Weekly Puzzle by Dilip D’Souza

How many leaves must you take from a book before their page numbers add up to 2020?

We’ve heard plenty about how 2020 has been a hard year in many ways for many of us. If that describes you, and if you’d like to do something about it, this puzzle gives you a chance to vent all your frustrations about this year. It asks you to indulge in some serious destruction.

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You’ve been warned.

Choose the least favourite book in your library. Any book at all, actually — all I ask is that you don’t choose an overly slim volume. Pick one that has at least 100 pages, preferably 150.

Now here comes the destructive part. Tear out exactly 15 pages at random from the book, making sure they all have page numbers printed on them. Add up the 30 page numbers you’ll see. Is your total 2020? If not, discard as many of the 15 pages as you like, rip out the same number from the book and add up the 30 page numbers again.

Repeat until either you get 2020 or the book is totally destroyed, whichever comes first.

Question: Which does come first?

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Answer: You’ll destroy the book first.

Take any given page you’ve ripped from the book. The page numbers on both sides are consecutive, thus one odd and one even. Their sum is odd, because when you add an odd and an even number, you get an odd number. You have 15 such odd totals, one for each page you’ve torn out. When you add 15 odd numbers — in general, when you add an odd number of odd numbers — your total remains odd. 2020 is even. Thus you will never get a total of 2020.

PS: I didn’t really mean for you to do the tearing. Please don’t tear up one of your books, however much you might dislike it. Give it away instead.