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Problematics | Wedding wheels
Two cars on a journey break down separately, and the one that is held up later completes the trip sooner. How long is the journey?
Puzzles involving speed and distance, like the one involving trains between Delhi and Amritsar, can never be monotonous because of the variety they offer. Each can be different from the previous one, and even similar ones can be made to look different. Take the following puzzle, for instance. You may have dealt with the same mathematical principles in previous puzzles, but I hope my new construction helps it remain a fun experience to solve.
#Puzzle 172.1
A couple planning to attend a wedding in the next town get into a quarrel just before the journey, so they set off in their separate cars. They start off at the same time and drive at the same steady speed, so they can see each other along the journey, occasionally exchanging an angry word between their cars. If they had continued at that speed, they would have reached their destination at 8 pm, which both husband and wife thought was an ideal time to reach a wedding reception.
They do not continue at the same speed, however, because fate strikes. Two hours after starting off, the wife’s car breaks down while the husband travels on, cheering the unfortunate turn of events. The wife steps out and does the repair work, which she finishes in 10 minutes. When she resumes her journey, however, it is at 30 kph, which is slower than her already slow original speed.
Much to her delight, the husband’s car too break down after travelling 30 km from the spot where she had to stop. He too takes 10 minutes to fix whatever is wrong, and he too completes the rest of the journey at 30 kph.
The husband reaches the wedding at 8:15 pm, the wife at 8:30 pm.
What is the length of the journey, and at which spots do the two cars break down?
#Puzzle 172.2
I first came across the following puzzle in Mindsport, the column Mukul Sharma wrote in The Illustrated Weekly of India during Pritish Nandy’s time as editor (neither of them is with us any longer, unfortunately). It was, however, probably not something MS had thought up himself, because I have found this in various other collections. The puzzle can be simply expressed (although MS made it a fun read with his inimitable style of writing).
You are alone in a room that is almost empty except for three occupants, you, a bar magnet, and a bar of iron that is identical in shape and size to the magnet. There is no magnetic material anywhere in the room or on your clothing.
Is it possible to determine which bar is iron and which is the magnet?
MAILBOX: LAST WEEK’S SOLVERS
#Puzzle 171.1
If the journey between Delhi and Amritsar takes n hours, the train that starts from Amritsar at the same time will cross this train from Delhi, and also all other trains leaving Amritsar up to (n – 1) hours after the Delhi-Amritsar train’s departure. That is, the trains leaving at the same time, 1 hour later, 2 hours later… (n – 1) hours later; these are 0 to (n – 1) or n trains.
The train that starts after n hours of our train’s departure will meet it at Amritsar and is to be ignored, and the train that left Amritsar n hours earlier will meet this train at Delhi and is also to be ignored. But trains that left (n – 1) hours, (n – 2) hours… 1 hour before from Amritsar will also cross this train. This total is (n – 1). Hence, in all, n + n – 1 = 2n – 1 trains will cross our train.
— Kanwarjit Singh, Chief Commissioner of Income-tax, retired
#Puzzle 171.2
Dear Mr Kabir,
No, the truck driver is not correct. To stay airborne, each pigeon exerts its full weight on the truck creating a reaction force as per Newton’s third law of motion. Thus the total weight exerted remains 1 tonne 20 kg.
— Shri Ram Aggarwal, Palam, New Delhi
***
Dear Kabir,
If the rear compartment is airtight there will be no change in weight. However, as it is impracticable to keep pigeons in an airtight compartment for long because they may die of suffocation (also, the driver unlocks the compartment thereby implying that inside air is in communication with the outside atmospheric air), the flapping of wings will cause air to flow outside the truck body. Then, there will be a partial reduction of reaction from the truck body as it will be borne by surrounding earth. But even in that scenario, the truck driver is wrong because the weight will still be more than 1 tonne.
— Yadvendra Somra, Sonipat
The question of birds flying in a container, in fact, has been the subject of scientific research. A Stanford University study 10 years ago demonstrated that birds continue to exert their weight when flying, but it is not always as simple as (weight of container) + (weight of birds).
Solved both puzzles: Kanwarjit Singh (Chief Commissioner of Income-tax, retired), Shri Ram Aggarwal (Delhi), Yadvendra Somra (Sonipat), Dr Sunita Gupta (Delhi), Shishir Gupta (Indore), Ajay Ashok (Delhi)
Solved #Puzzle 171.1: Anil Khanna (Ghaziabad), Professor Anshul Kumar (Delhi), Sabornee Jana (Mumbai), YK Munjal (Delhi)
Solved #Puzzle 171.2: Nitin Trasi (Sydney)
