Problematics | A spider’s tale, with a nod to Pythagoras - Hindustan Times
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Problematics | A spider’s tale, with a nod to Pythagoras

Nov 06, 2023 05:48 PM IST

Help a spider cross the street without spinning a web. She has two poles to navigate, with some elementary calculations.

Spiders, I think, build their webs from higher to lower altitudes, but not the other way around. They do not, for example, build a web from the floor of a room to the ceiling; they would rather climb the wall before descending by the web.

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

If any of my readers is an arachnologist, please let me know if I have got my facts wrong. Not that it really matters. In the following puzzle, at least, you can assume that our protagonist never builds a web in the ascending direction; in fact, she rarely uses the web at all. She prefers to climb.

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Puzzle 63.1
Puzzle 63.1

#Puzzle 63.1

Once upon a time, long before the metric system was introduced, a spider sat at the foot of a building on one side of a busy street, wanting to cross to the other side but unwilling to brave the heavy traffic. The only thing to do is to climb a building and descend to the other side, she thought.

She noticed the end of a pole, 500 inches long, at the very point where she was musing. The other end of the pole rested on the wall of another building, which was on the other side of the street.

Looking straight up, the spider observed another pole, 375 inches long, one end resting on the wall of the nearer building at a point 225 inches directly above her. Its other end was on the opposite side, touching the bottom of the farther building. The two poles touched each other at a point above the street.

“What if,” the spider mused, “I climbed the nearer pole diagonally, reached the point where it touches the other pole, and then descended the second pole to the bottom of the other building? I need not depend on a web-based solution after all.”

She followed that plan. What distance did she travel?

#Puzzle 63.2
#Puzzle 63.2

#Puzzle 63.2

These are anagrams of five English-language movies (Hollywood and/or British productions). The encircled letters form another anagram, which will give you the name of a superstar who appears in all five movies. Easy-peasy.

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#Puzzle 62.1

Hi Kabir,

Let the first number be x and the second be y. The 10 numbers will be:

x, y, x + y, x + 2y, 2x + 3y, 3x + 5y, 5x + 8y, 8x + 13y, 13x + 21y, 21x + 34y

The sum of these 10 numbers is 55x + 88y = 11(5x + 8y)

Here 5x + 8y is the seventh number. So, the grand total is 11 times the seventh number.

— Rachna Jain, Delhi

#Puzzle 62.2

Hi Kabir,

Let two hourglasses be HG₁ (11 minutes) and HG₂ (7 minutes). Start with the upper bowls full in both hourglasses.

  • Invert HG₂ when its upper bowl is emptied.
  • Invert HG₂ again when the upper bowl of HG₁ is emptied. HG₂ now has 4 minutes of sand in its upper bowl.
  • When the upper bowl of HG₂ is emptied again, the total time measured is 11 + 4 = 15 minutes.

— Abhinav Gupta, Rewari

Note: Readers who missed the significance of the seventh number are not credited with solving Puzzle #63.1. Those who described hourglass operations that took 22 minutes overall in order to measure 15 minutes are not credited with solving Puzzle #63.2.

Solved both puzzles: Rachna Jain (Delhi), Abhinav Gupta (Rewari), PK Mishra (director, retired; DGS & D), Prof Anshul Kumar (Delhi), Kanwarjit Singh (Chief Commissioner of I-T, retired), Dr Sunita Gupta (Delhi), Amit Khanna (Fremont, California), Ankur Anand (Ranchi), Sushma Pandhi (Chandigarh), Anil Khanna (Ghaziabad), Ayush Tandon (Delhi Technical University), Deepak Nayyar (Delhi), Neel Bainsla (Delhi), Rohit Khanna (Noida), Akshay Bakhai (Mumbai), Sumit Malhotra (Delhi), Harsh Ozare (Kongaon), Shri Ram Aggarwal (Delhi), Vivek Aggarwal (Bangalore)

Solved #Puzzle 62.1: Sudip Khanna (Fremont, California), Yadvendra Somra (Sonipat), Rajesh Bansal (Noida), Amar Lal Miglani (Mohali), Radhika Joshi (DPS Vasant Kunj), Sunita & Naresh Dhillon (Gurgaon), Amardeep Singh (Meerut), Akanksha BS Sharma (Delhi)

Solved #Puzzle 62.2: Ar Kamal Passi (CPWD), Group Captain RK Shrivastava (retired; Delhi), Rakesh Sahni (Noida), Sabornee Jana (Mumbai), Rohit Sahay (Delhi), Bhasker Mundhra (Ghaziabad), Vineet Kumar Dargan (Delhi), Dr Sameer Bhatia (Delhi), Vivek Jain (Baroda), Shishir Gupta (Indore), Harsh Sisodiya, Dhruv Kundrai, Ankush Goyal, Abhineet Jaiswal

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

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  • ABOUT THE AUTHOR
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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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