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For The Mathematically Inclined

Anil Saigal
06/07/2010

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?

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?

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Problems from 05/27/10

PROBLEM # 1

Teacher:     You appeared for quizzes in 10 subjects, and your average marks in them were 79.
Student:     How did I fare in English?
Teacher:     Well, your average in English Language and English Literature is 43.
Student:     So, how was my performance in the remaining subjects?
Teacher:     I am sure you can figure that out for yourself.

Can you help the student find his average marks in the remaining subjects?

88.

PROBLEM #2

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 5 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 8 hours.

What fraction of the tank (initially empty) will be filled in 2.45 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

1.00.

Congratulations to Kishore Balsara, Lalit Doshi, Sophia Farooqui, Suhas Joglekar, Arun Lahori, and Bharath Venkataraman, who were winners of the last set of puzzles.

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Fig. 1

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