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For The Mathematically Inclined

Anil Saigal
06/17/2010

PROBLEM # 1
Haretown and Tortoiseville are 70 miles apart. A hare travels at 8 miles per hour from Haretown to Tortoiseville, while a tortoise travels at 2 miles per hour from Tortoiseville to Haretown. If both set out at the same time, how many miles will the hare have to travel before meeting the tortoise en route?

PROBLEM #2
A cylinder 75 cm high has a circumference of 20 cm (Fig. 1). A string makes exactly 5 complete turns round the cylinder while its two ends touch the cylinder's top and bottom. How long is the string in cm?

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Please send your solutions to mr.asaigal@gmail.com.

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Problems from 06/10/10

PROBLEM # 1

Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 12 years as an old man, then how many years did he spend as an active man?

SOLUTION

48 years.

PROBLEM #2

In Fig. 1 consider 25 lines drawn at a tangent

to an ellipse. The lines break up the plane into several regions, some bounded (i.e., enclosed) and others unbounded. How many unbounded regions are there?

SOLUTION

50.


Congratulations to
Kishore Balsara, Sitaram Chandawarkar, Akshay Gowrishankar, Ranganath Nayak and Sandeep Shankar, who were winners of the last set of puzzles.



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