Problematics | Once upon a time in the wheels

Oct 10, 2022 12:34 PM IST

There is a gem of a puzzle hidden in old cinema shots of a moving stagecoach.

A still from Once Upon a Time in the West (1968). 
A still from Once Upon a Time in the West (1968). 

Many readers will instantly recognise the photograph above: it’s a still from Once Upon a Time in the West (1968).

Half an hour into the iconic Western, the newlywed Jill, played by Claudia Cardinale, steps out of a train and is surprised to find no one to receive her at the station. Even for a movie as widely watched as this one, we cannot give out spoilers on why no one receives her. All that needs to be said is that Jill boards the wagon, or stagecoach, that you see in the picture.

There is a gem of a puzzle hidden in old cinema shots of a moving stagecoach. The question is: does it hold in the scene above? After replaying it several times, I think it does. If you have a copy, you can play that scene and tell me what you noticed. Even if your observations are different from mine, the puzzle below will still hold because of the numbers chosen.

Puzzle 7.1 
Puzzle 7.1 
Puzzle 7.2
Puzzle 7.2
Mailbox: Last week’s solvers 

#Puzzle 6.1


This question can be easily solved using Venn diagrams or principles of relations.

The number of people eating only an aebleskive is 7; the number of people eating only a baklava is 8; the number of people eating only clafoutis is 6; and the number of people eating all three is 32.

I’m eagerly looking forward to next week’s puzzles.

— Ananyaa Priyadarshini, Carmel Convent School, Chandigarh

#Puzzle 6.2 


Since every gangster deposited an equal amount, first we will have to look at the possible factors of ₨ 63,59,23,909. There are only 2 possible factors, 797 x 797897.  We may safely assume that there are 797 gangsters, and each one collected say 8 lakh. Thus, we may say the two-way fare is 8 lakh – 797897 = 2103, or one-way fare is 1051.50. 

— Anil Kumar Goyal, New Delhi 

Dr J S Sabharwal from Mohali gives the above solution as well as an alternative combination: a train fare of 525.75 each for 1,594 gangsters who deposit 4 lakh each (before deduction). There are other combinations that are mathematically possible, but not all of them make practical sense. Bizarre findings such as 7,97,897 gangsters boarding a single train, therefore, do not count among the correct answers. 
Solved both puzzles: Gopal Menon (Mumbai), Sandra Danisha (Podar International School, Kalyan), Anil Goyal (Delhi), Biren Parmar (Bay Area, California), Madhuri Patwardhan (Thane), Simran Kaur (Delhi), Dr J S Sabharwal (Mohali), Vinod Mahajan (Delhi), Jasvinder Singh (Nabha), Sahil Vij (Bahadurgarh) 
Solved #Puzzle 6.1 only: Shivika Gupta (Delhi), Ananyaa Priyadarshini (Chandigarh), Aishwarya Sreejith (Mumbai), Indu Jhingan (Delhi), Himanish Kumar (Delhi), Hezail Sharma (Faridabad), Raunaq Nayar (Delhi), Atul Datt, Nupur Joshi (Delhi), S C Dogra (Delhi), Shishir Gupta (Indore)  
Solved #Puzzle 6.2 only: Shashank Joshi (Mumbai), Jasleen Kaur (Delhi) 

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

Enjoy unlimited digital access with HT Premium

Subscribe Now to continue reading

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

Story Saved
Saved Articles
My Reads
My Offers
Sign out
New Delhi 0C
Friday, March 24, 2023
Start 15 Days Free Trial Subscribe Now
Register Free and get Exciting Deals