Problematics | Swimmers’ meetings and Asimov’s pretty numbers

Mar 27, 2023 02:12 PM IST

This week, we have challenging puzzles, one involving speed and distance and the other, a list by Isaac Asimov, giving both our puzzles a touch of unusualness. Good luck!

Was last week’s puzzle based on Jamie Lee Curtis’s name exceptionally difficult? I did not think so when I planned it, hoping that it would be mildly challenging, but an uncharacteristically low number of correct replies indicates that many readers found it tougher than usual.

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

Last week’s other puzzle, which involved speed and distance, was easier but some readers made mistakes here, too. Before going into that, here’s a more challenging puzzle involving speed and distance.

#Puzzle 31.1:

#Puzzle 31.1.
#Puzzle 31.1.

An unusual race between two swimmers takes place as follows. Both will travel the length of a pool and back, but they will take off from opposite ends. The race will be won, obviously, by the swimmer who returns to her starting point before the other one does.

The swimmers take adjacent lanes in the pool and, as previously agreed, take off at the same instant, but from opposite ends. As they swim towards each other’s end, it becomes obvious to the audience that one of them is faster than the other. They cross each other and, after some time, the faster swimmer reaches the opposite end. She loses not an instant in turning back and beginning her return leg.

A little more time passes before the slower swimmer reaches the end opposite to the one she had started from. She, too, loses no time in turning back and beginning her second leg. The two swimmers cross each other again, and carry on, taking the race to its predictable conclusion.

The first time the two swimmers cross each other, they are 22 metres from one of the ends. The second time they cross, they are 16 metres from the other end.

Assuming that both swimmers maintain their respective constant speeds, what is the length of the pool?

#Puzzle 31.2:

In his book, The Secret of the Universe: Revelations in Science, Isaac Asimov compiles a rather unusual list (which gives a touch of unusualness to both our puzzles this week). Only a part of Asimov’s list is reproduced below:

Earth— Neptune 14.4
Mars 1.95Pluto0.72

Asimov’s book, and therefore the list, came out at a time when Pluto was considered a planet. He did not intend it as a puzzle, because he specified what the numbers meant.

“What’s the good of this list?” Asimov wonders. “Well, it’s pretty, and I don’t know that it exists precisely in this form anywhere else. I like things that are pretty, and orderly, and different. After all, as I told you, I’m peculiar.”

The “good of this list” is that it provides us the fodder for a puzzle. Can you figure out the basis for those numbers? And what number would you enter against Earth?

Mailbox: Last week’s solvers

#Puzzle 30,1 and #Puzzle 30,2,
#Puzzle 30,1 and #Puzzle 30,2,
Solved both puzzles: Amardeep Singh (Meerut), Sunita & Naresh Dhillon (Gurgaon), Sunita Gupta (Delhi), Mayobhav Pathak (Gurgaon), Shishir Gupta (Indore), Sabornee Jana (Mumbai), Jayesh Sharma (Mandi Gobingarh), Rahul Agarwal (Bay Area, California), Harshit Arora (Delhi)
Geetansh Gera, Hardeep Singh, Raghav Khapre, Jasvinder Singh and Nipun Bamania have solved the first puzzle, while Dr Sunita Gupta and Tripti Bucha have solved the second.

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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