Problematics | How to arrange your bookshelf - Hindustan Times

Problematics | How to arrange your bookshelf

Jan 22, 2024 08:00 AM IST

Arrange your books vertically and you run out of space. Stack them up flat on their backs and your shelf is left with unused space. How many books are new?

The photograph accompanying the first puzzle is of my own bookshelf, clicked years ago. The point here is that, as any book lover knows, there can be several different ways of arranging your books on your shelf. One is to set each book up vertically like libraries do so that any borrower can easily take it out without disturbing the other books. Another way is to stack them one atop the other, so that you can have a number of such stacks from left to right, depending on the breadth of your shelf.

Welcome to Problematics!(Shutterstock)
Welcome to Problematics!(Shutterstock)

It can be debated which one of these arrangements allows you to accommodate more books. If your shelf is deep enough, which it usually is in order to accommodate large volumes such as dictionaries and encyclopaedias, then stacking them probably uses your space more economically. I use a mixture of both, as you can see from the photo, but that is beside the point. In the library described below, the workers follow the usual tradition of books lined up vertically.

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Until today.

#Puzzle 74.1

#Puzzle 74.1
#Puzzle 74.1

“That’s a whole lot of books,” said Booker, having unwrapped the scores of packets that had arrived.

“As it should be in a library,” Bookie told him. “Stop cribbing and start arranging them.”

“Think we have enough space? We are already tightly packed as it is.”

“Cribbing again,” Bookie repeated the rebuke. “We’ll know only if we try, won’t we?”

It was not long before they had filled all the space remaining on their shelves.

“That’s 50 books with no place to go,” said Booker, who sounded triumphant. “I told you we were short of space, didn’t I?”

“That doesn’t mean we don’t arrange them,” said Bookie. “Let’s lay them flat this time, one on top of the other.”

“What, all our books?”

“No, only the new books, silly,” Bookie said.

The two laid out the new books once more, this time with space to spare.

It was Bookie’s turn to be triumphant. “We can still accommodate 150 new books when the next batch arrives.”

“Only if we arrange them flat like this,” Booker mourned. “Readers will struggle to pull out the lowermost volumes.”

“A new bookcase or two would help,” Bookie agreed. “But I told you we had enough space for today’s lot, didn’t I?”

Booker, beaten, needed to bounce back. And how else could he do that but by setting a puzzle?

“Did you notice,” he said, “that we accommodated three times as many books per shelf the second time than the average/shelf we had managed in the vertical arrangement?”

“Who cares?” Bookie snapped.

“You should,” Booker smiled. “You will need that information to work out the number of new books we arranged today.”

“Why work it out? It’s all listed here…” Bookie reached for the catalogue, but Booker snatched it away before he could reach it.

“No, calculate it,” Booker said. “If you are able to,” he added, triumphant once more.

Bookie failed. Can you help him?

#Puzzle 74.2

Ant-Man, Iron Man and Spider-Man are acting in three films called Scream, Dracula and Halloween. Each actor appears in one film only.

“Have you noticed,” Ant-Man observes, “that none of us is acting in a film whose title has the same number of letters as the actor’s name?”

“Indeed,” replies one of the other two actors, who is playing the lead in Dracula.

Who is acting in which film?



#Puzzle 73.1

Solution Puzzle 73.1
Solution Puzzle 73.1

# Puzzle 73.2

Hi Kabir,

This is a tricky one because the length of the word is not specified. Below are a few possible solutions:


M and W are the only ones that turn into each other when turned upside down. To be honest, even that is not really the case because M has vertical outside lines whereas W has slanting ones.

The other letters that remain identical when turned upside down are X, Z, H, S, O, I

It is probable that there are more words using MWXZHSOI as letters (some even multiple times in the word) which read the same upside down. But since the puzzle asked for one example (without specifying the length), the above list should be sufficient.

As regards the question about whether the solution is unique, the answer is NO.

— Akshay Bakhai (Mumbai)

As a matter of fact, I should have specified the length of the word, but it got left out. According to the book of puzzles where I found this one, there is only one word of four letters that fits the description, which is NOON.

Although I missed the letter count, the puzzle became more interesting as readers sent various options. As it turns out, NOON is the only acceptable four-letter option received. Group Captain RK Shrivastava (retired) asserts that the longest possible word is SWIMS, just five letters, and indeed no one has sent any longer option.

Solved both puzzles: Dr Sunita Gupta (Delhi), Akshay Bakhai (Mumbai), Yadvendra Somra (Sonipat), Group Captain RK Shrivastava (retired; Delhi), Sundarraj C (Bengaluru), Shishir Gupta (Indore), Kanwarjit Singh (Chief Commissioner of Income-Tax, retired)

Solved #Puzzle 73.1: Ajay Ashok (Mumbai)

Solved #Puzzle 73.2: Geetansha Gera (Faridabad), Jaikumar Inder Bhatia & Disha Bhatia (Ulhasnagar, Thane)

Problematics will be back next week. Please send in your replies by Friday noon to

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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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