Problematics | Who wins this race? - Hindustan Times

Problematics | Who wins this race?

Feb 12, 2024 08:00 AM IST

Five athletes in their lanes, each from a different country and dressed in her favourite colour. Who is wearing what, and who wins?

After a couple of tough puzzles in consecutive weeks, we had a (relatively) easy one last week. As YK Munjal notes: “In your attempt to present easy puzzles, the first one is just mathematics. Anyone who is good at mathematics will solve it in a jiffy.” Point taken, but the idea of this column has always been to present puzzles that are fun to solve, with toughness/easiness a side issue. “Neither too easy nor too hard” remains our motto.

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

Perhaps the following puzzle belongs to that category. Like last week, we are about to witness a race among athletes, but this time there is no mathematics involved, just logic. Yes, it’s an Einstein puzzle.

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#Puzzle 77.1

Meet five athletes from five countries, which are, in alphabetical order: Afghanistan, Albania, Angola, Argentina and Australia. They are on the racetrack, each wearing track attire in her favourite colour: beige, black, blue, brown and burgundy. They are all named after Indian athletes: Ashwini, Dutee, Hima, Shiny and Usha. To complete the introductions in alphabetical order, their surnames are Devers, Griffith, Jones, Kersee and Ottey.

1. Jones is in Lane 1, Ottey in Lane 2, Shiny in Lane 3, the Albanian in Lane 4, and Hima in Lane 5.

2. Usha is from Afghanistan and Ottey is from Australia.

3. The Albanian finishes third in the race.

4. Shiny finishes immediately ahead of Kersee who, in turn, finishes immediately ahead of the athlete wearing black.

5. Usha finishes immediately behind the athlete wearing beige, while the athlete in blue finishes immediately behind the Argentinian.

6. Ashwini’s surname is Devers.

7. The athlete in Lane 3 and the Angolan finish close to each other. One of them is wearing blue while the other is in brown.

To prevent any misunderstanding: (a) when one athlete is “immediately behind” or “immediately ahead of” another athlete, it means there is no other athlete between them; (b) when two athletes finish “close to each other”, it means, again, that there is no athlete between them.

Who is from where, what are their full names, who runs in which lane, and what are their positions at the end of the race? These solutions work best in tabular form.

#Puzzle 77.2

This crossword without clues is not a word puzzle, but another one that you solve with logic and elimination. The crossword's entries are the 22 languages under the 8th Schedule of the Constitution of India.

Filling it up is not as difficult as it may appear (you may need to take a printout, though). I think the solution is unique, but you are welcome to send any alternatives you may find.


Readers, here's another introduction. Sampath Kumar V, who used to solve my puzzles regularly almost a decade ago, has now joined us here. Welcome aboard, Sampath, and thank you also for introducing a couple of new readers to Problematics.

#Puzzle 77.2
#Puzzle 77.2
Solution #Puzzle 76.1
Solution #Puzzle 76.1

#Puzzle 76.1


Dear Mr Kabir,

Taking metres, seconds and m/s as the units, 10.8 km/hour is the same as 3 m/s, and 3.6 km/hr = 1 m/s.

Variable 1st 2nd Last

Time (sec) t t + 30 t + 50

Speed (m/s) s s – 3 s – 4

The total distance covered by each runner is the same:

(s)(t) = (s– 3)(t + 30) = (s– 4)(t + 50)

Solving, we get s = 8 m/s and t = 50 seconds. Therefore, distance = 8 x 50 = 400m. That is the length of the track. The time and speed of each runner is shown in the table.

— Sampath Kumar V, Coimbatore


#Puzzle 76.2

Hello Kabir,

For the Wordle puzzle, two possible solutions are BRIBE and EERIE. There may be more, so no unique solution.

— Biren Parmar, Bay Area, California


Only the letters E, R and I can be used, all these at places other than indicated. The only other available letters are B and Q. But Q cannot be used as U is not there. Hence, the only two possible words are BRIBE and EERIE

— Kanwarjit Singh, Chief Commissioner of Income Tax (retired)

I too think BRIBE and EERIE are the only two words possible. Even if there are other possible solutions, which is unlikely, it does not matter because two solutions are enough to answer the original question: Do you have enough information to deduce the word correctly? The answer is no because you can already see two possibilities.

A few readers have got only one of the two words and a couple of them have asserted that the solution is unique. Unfortunately, they cannot be listed among the correct solvers.

Solved both puzzles: Santosh Kumar V (Coimbatore), Biren Parmar (Bay Area, California), Kanwarjit Singh (Chief Commissioner of Income Tax, retired), Sanjay S (Coimbatore), Dr Sunita Gupta (Delhi), Amarpreet (Delhi), Akshay Bakhai (Mumbai), Professor Anshul Kumar (Delhi), Ajay Ashok (Mumbai), Shri Ram Aggarwal (Delhi), Group Captain RK Shrivastava (retired; Delhi)

Solved Puzzle #76.1: Y K Munjal (Delhi), Shishir Gupta (Indore), Anil Khanna (Ghaziabad)

Solved Puzzle #76.2: Sundarraj C (Bengaluru)

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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