Problematics | Crossing the desert without enough fuel

Jul 17, 2023 12:07 AM IST

A puzzle in which you make a long trip across forbidding terrain, but will need more supplies than you can possibly carry.

Looking at back issues, we can see that there has been a wide variety among the puzzles that have entertained us over the last several months: speed and distance, deceptively simple arithmetic, anagrams, logic, probability, Einstein puzzles…

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

There are a few puzzle families, however, that we have not yet visited in this column. One is the “desert crossing” type, in which you make a long trip across forbidding terrain, but will need more supplies than you can possibly carry. Let’s give it its Problematics debut this week.

#Puzzle 47.1

#Puzzle 47.1(Mohit Suneja)
#Puzzle 47.1(Mohit Suneja)

To make the trip possible, the motorists devise a way to give and take fuel from one another. If a vehicle wants to make the crossing, one or more other vehicles will accompany it for some distance. At some point, carefully calculated, one or more vehicles will transfer some of their fuel to one or more others. Those making the transfer will return to the station with their remaining fuel, while the rest will carry on in the direction of the town.

Farther ahead, more fuel transfers and more return trips may take place, or may not. The fuel station’s branch in the town, too, can send other vehicles out into the desert to meet the vehicle(s) from the station, transfer some fuel, and escort them back to town.

One vehicle needs to travel from the station to the town. There can be a number of ways to complete the trip. So, use the help of the minimum number of vehicles that is necessary, and spend as little fuel as possible overall. The most economical solution wins.

#Puzzle 47.2

This appeared in Mukul Sharma’s column Mindsport in The Illustrated Weekly of India sometime in the early 1990s. I do not know whether Dear MS, as readers used to address him, created the puzzle himself or picked it up from somewhere. It involves an unusual arrangement of words, which I am repeating from memory:

time flies i cant theyre too fast

Punctuate the above to form a meaningful English sentence or sentences.


#Puzzle 46.1

Just turn the pile of 20 cards over and the number of face-up cards will be the same in both piles. Reasoning: if the number of face-up cards in the pile of 20 is x, the number of face-up cards in the pile of 32 will be (20 – x). The number of face-down cards in the pile of 20 is (20 – x), which become face-up when we turn this pile over.

— Mukesh Arora, Gurgaon

The above puzzle, while interesting, could have been made a little more difficult. Having realised this in hindsight, I shall try and bring you another version at a later date.

#Puzzle 46.2

#Puzzle 46.2
#Puzzle 46.2

These are films made by Alfred Hitchcock. The 15 letters encircled, when rearranged, give the name ALFRED HITCHCOCK (6, 9). I found this easy probably because I am a huge fan of Hitchcock and an avid cryptic crossword solver.

— Akshay Bakhai, Mumbai

Solved both puzzles: Mukesh Arora (Gurgaon), Akshay Bakhai (Mumbai), Dr Sunita Gupta (Delhi), Dr Manu Gupta (Delhi), Anil Kumar Goyal (Delhi), Sunita & Naresh Dhillon (Gurgaon), Akshay Khanna (Bangalore), Amardeep Singh (Meerut), Gaurav & Kabir Gupta (Indirapuram), Ravishankar Kulkarni (Mumbai), Akshat Balyan (Sonipat), Vinod Mahajan (Delhi), Adeep Atey (Kalyan), Simran Pushkarna & Sarthak Pushkarna (Delhi), Sanjay Gupta (Delhi), Gaurav Gummaraju (Navi Mumbai), Madhuri Patwardhan (Thane), Subrata Chakravorty (Gurgaon), Geeta Arora & Amarnath Arora (Delhi), Prof Anshul Kumar (Delhi), Shankar Subramanian (Mumbai), Ajay Ashok (Mumbai), Dipali Gupta (Delhi), Shishir Gupta (Indore), Saurish Seksaria (Mumbai)

Solved #Puzzle 46.1: Yadvendra Somra, Shruti M Sethi, Aarika Goel, Vishesh Sharma, Anil Khanna, Jawahar Lal Aggarwal, Nehil Mahindru, HP Choudhury, Kanwarjit Singh, SR Aggarwal, Ayush Chaturvedi, Aziza, Aditya Prakash, Manas Zanwar.

Solved #Puzzle 46.2: Dr Nakul Makkar, M Prakash, K Hema, Sandeep Bhateja, Ramesh Dhas, Narendra Prasad.

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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