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For The Mathematically Inclined

Anil Saigal
10/22/2009

PROBLEM # 1

You need to make a pizza box. You know that the box needs to be two inches deep, it needs to be a square, and have a volume of 512 cubic inches. What is the size of the original cardboard sheet?

PROBLEM #2

A goat is tied to the corner of a 5-by-4-meter shed by a 8-meter piece of rope. Rounded to the nearest square meter, what is the area grazed by the goat?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-102909 as the subject line. Please include your full name in the text of the main message. Everyone with the right answer will be acknowledged in the next issue of Lokvani.

Please do not post your solution in Post Comments. No credit will be given for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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Problems from 10/15/09

PROBLEM # 1

Suppose f(x+3) = 3x2 + 7x + 4 and f(x) = ax2 + bx + c. What is a+b+c?

SOLUTION
2.

PROBLEM #2

Let a + ax + ax2 + ax3 +...  and a + ay + ay2 + ay3 +... be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is x, and the sum of the second series is y. What is x + y?

SOLUTION
1.

Congratulations to Debjyoti Banerjee, Sitaram Chandawarkar, Chandran Elumalai, Shailesh Goregaokar, Dattatraya Joshi and Prabhakar Nadkarni, who were the winner of the last set of puzzles.



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