Problematics | Untold story about a hare and a tortoise

This week, one of the two puzzles may include some information you don’t really need. Good luck!

I have sad news to share: we have lost one of the regular contributors to this column. Gopal Menon of Mumbai, who rarely missed any of my puzzles, and whose solutions I would wait expectantly for, passed away suddenly on February 3. The news comes from his daughter Roshni, writing from Gopal’s email address.

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On January 30, Gopal’s detailed solution to #Puzzle 22.1 (‘The puzzling truth about cats and dogs’) appeared here in detail. As I noted then, his solution was better than my own, pointing out that I had provided more information than was necessary for solving the puzzle.

This week, too, one of the puzzles may include some information you don’t really need. If it does, Gopal would likely have spotted this even if I hadn’t mentioned it. We shall miss him.

#Puzzle 26.1.

A fast hare racing a slow tortoise gets so far ahead that he falls prey to overconfidence and takes a nap along the way, only to be overtaken by the tortoise. The hare wakes up and makes a sprint in an effort cover up lost ground.

The tortoise, still ahead, reaches an avenue lined with 59 pairs of trees, each pair spaced 25 m from the next, with a separation of 25 m between the start of the avenue and the first pair of trees, and again 25 m between the last pair of trees and the end of the avenue. Some distance ahead of the end of the avenue is the finish line of the race.

Running along the avenue, the tortoise, who is also a mathematician, calculates: “I am 1½ times as far from the 11th pair of trees as I am from the 10th.”

Then he looks back over his shoulder and sees the hare closing in. “If I turn back and run towards him (which I won’t do, of course) and if both of us maintain our speeds, we will meet at the start of the avenue. But if we continue ahead at our respective speeds, the hare and I will reach the end of the avenue at exactly the same moment.”

It is at the midpoint of the avenue that the tortoise finds an inspired burst, doubling his speed for the rest of the race. He reaches the finish line at the same moment when the hare reaches the end of the avenue.

How far behind was the hare when the tortoise won?

#Puzzle 26.2:

You can solve the above puzzle using all the information provided. But, could you also ignore some of the information and still reach the same solution?

Mailbox: Last week’s solvers:

#Puzzle 25.1 solver.

#Puzzle 25.2:  Dear Kabir Sir,  The four cities are:   BARASAT, MUMBAI, NEW DELHI, RANCHI  — S Anju Iyengar, Faridabad

Solved both puzzles: Akshun Gulati (Delhi), S Anju Iyengar (Faridabad), Dr Sunita Gupta, Rohit Khanna (Noida), Jasvinder Singh (Nabha), Harshit Arora (Delhi), Veer Bhadra Singh (Rajasthan), Vasu Handa (Sonipat), Shishir Gupta (Indore), Dr Nakul Makkar (Noida), Ravi Sondhi & Rudra Sondhi (Gurgaon), Rahul Agarwal (Bay Area, California), Amardeep Singh (Meerut), Musarrat Rai Handa (Faridabad)

Solved #Puzzle 25.1: Aarika Goel (Gurgaon), Shibha Jain (Mumbai), Amit Kumar Gupta

Solved #Puzzle 25.2: Tejwinder S Anand (Gurgaon), Vinod Kumar Vij (Rohtak), Shirin Samuel (Bangalore), Swati Tandon (Delhi), Sudesh Dogra (Delhi), Sini Thomas (Delhi), Avni Nayak (Airoli), Ajay Chandwal, Raj Kumar Yadav, Sunita & Naresh Dhillon (Gurgaon), Dr Amanpreet Kaur (Kapurthala), Vinod Mahajan (Delhi), Jaikumar Inder Bhatia (Ulhasnagar, Thane), Nipun Bamania (Mumbai)

Problematics will be back next week. Please send in your replies before Friday noon to problematics@hindustantimes.com