Problematics | 400m contests away from the champions - Hindustan Times

Problematics | 400m contests away from the champions

Sep 04, 2023 01:10 PM IST

Given the times when two runners meet and cross each other along a track, can you work out their respective speeds?

The world record for the men’s 400m is 43.03 seconds, clocked in the 2016 Olympics. For women, the world record is 47.60 (1985 World Cup) while the Olympic record is 48.25 (1996). Among Indians, the men’s and women’s 400m records are 45.21 and 50.79 seconds respectively.

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

That gives us the range of timings within which we must set our puzzle. It’s about athletics, as you might have guessed, but these runners are nowhere near as fast as the champions.

#Puzzle 54.1
#Puzzle 54.1

A self-proclaimed runner sets up a coaching centre. He lays a 390m track but tells everyone it is 400m, so that his trainees would believe their timings were for the full distance when they would actually have completed 10m less.

“Let’s race,” he tells a novice, who is not particularly talented. They set off together. Needless to say, the coach completes the 390m lap before the novice. Both of them, however, keep running. Round and round they go, completing several laps. Remarkably, each one maintains his own constant speed throughout. When the coach finally catches up with the slower one, it is exactly 6 minutes 30 seconds after they had started off together.

“Rest now,” the coach instructs the exhausted novice.

When they resume, they try a different format. Once again, they start off together from the same point, but this time they run in opposite directions. Once again, each runner maintains his own constant speed, which is exactly the same as his speed during the previous round of practice.

Inevitably, the two meet somewhere along the course of the track. It’s exactly half a minute since they had set off in their respective directions.

What are their respective speeds, and how long would each one take to complete an actual 400m run?

#Puzzle 54.2

One of the smallest known organisms is a bacterium called Pelagibacter ubique, with an average cell diameter of 120 to 200 nanometres (for ease of doing calculations, take it as 0.00013927mm). The largest object in our Solar System, on the other hand, is the Sun, the subject of Isro’s Aditya L1 probe. That’s 1.3927 million km in diameter.

A boon granted by a wizard enables a specimen of Pelagibacter ubique to grow in size at a constant rate. That is to say, it will double in size every day until it chooses to stop. The wizard also grants the bacterium conditional immortality: it will never die as long as it is smaller than the Sun, but will vanish into thin air the day it reaches or crosses the size of the Sun.

After how many days must the bacterium push the STOP GROWING button?

Mailbox: Last week’s solvers

#Puzzle 53.1
#Puzzle 53.1

#Puzzle 53.1

Hi Kabir,

The cards in order from left to right are: King of Clubs, Jack of Hearts, Ace of Spades, Queen of Diamonds.

— Nikhil Yadav, Gurgaon

#Puzzle 53.2

Dear Kabir,

Some possible solutions are: SIBYL, SILKY, SYLIS

— Aparjita Shrivastava, Kolkata

SIBYL (an oracle, prophetess or sorceress), SILKY, and SYLIS (plural of SYLI, a former monetary unit) are the only words acceptable. The alternative spelling SYBIL (a proper name) does not count. Some readers have offered YLIDS (plural of YLID, a kind of molecule) but that cannot count either, because no standard dictionary has included the word yet. Anyone who has offered at least one word among SIBYL, SILKY and SYLIS is acknowledged below.

Solved both puzzles: Nikhil Yadav (Gurgaon), Aparajita Shrivastava (Kolkata), Prof Anshul Kumar (Delhi), Rajesh Bansal (Noida), Anil Khanna (Ghaziabad), Shawn Jacob (Mumbai), Yadvendra Somra (Sonipat), Akshay Bakhai (Mumbai), Raunaq Nayar (Delhi), Dr Nakul Makkar (Noida), Group Captain RK Shrivastava (retd, Delhi), Simran Pushkarna & Sarthak Pushkarna (Delhi), Charvi Brajpuriya (Faridabad), Nikki Yadav (Gurgaon), Richard D’Souza (Mumbai), Bimal D Jhaveri (Mumbai), Vinod Mahajan (Delhi), Sunita & Naresh Dhillon (Gurgaon), Amardeep Singh (Meerut), Abhishek Garg (Chandigarh), Harshit Arora (IIT Delhi), Sandeep Bhateja (Hoshiarpur), Sankaran KB (Chennai), Sridhar Srinivasan, Anjali Nadkarni, Narendra Prasad

Solved #Puzzle 53.1: Shruti M Sethi (Ludhiana), Sushant Anand & Smriti Bhatnagar (Delhi), Nipun Kumar (Mumbai), Ajay Ashok (Mumbai), Shri Ram Aggarwal (Delhi), Vivek Aggarwal (Bangalore), Geetansha Gera (Faridabad), Shashi Bahadur

Solved #Puzzle 53.2: Ananyaa Priyadarshini (PEC Chandigarh), Anish Nair (Mumbai), Kanwarjit Singh (Delhi), Sumit Malhotra (Delhi), Y K Munjal (Delhi), Shishir Gupta (Indore), Sairam, Soumil Mukhopadhyay, V Anand, Adeep Atey, Shriya Seshia

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

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