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For The Mathematically Inclined


Anil Saigal 12/22/2005
FOR CHILDREN
PROBLEM # 1 If the difference of two numbers is 9 and their product is 14, what is the sum of the squares?
FOR GROWNUPS
PROBLEM # 2 Given f(x) = (xa) (xb)^2 ln(x^c) and 1<a<b<c For what values of x is f(x) positive?

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SOLUTIONS TO PROBLEMS ON 12/15/05
FOR CHILDREN
PROBLEM # 1 Each tire for my monster truck will last exactly 14,000 miles. How many spares do I need so I can use the fewest number of tires in a total of 21,000 miles? Explain how you got your answer.
SOLUTION 2.
FOR GROWNUPS
PROBLEM # 2 You begin to solve a complicated math problem between 4:00 and 5:00 p.m. when the clock's hour and minute hands are together (on top of each other). You finish the problem when the minute hand is exactly opposite the hour hand. (Please try to answer to the nearest second!)
Part 1: How many minutes does it take you to solve the problem? Part 2: At what time do you finish the problem?
SOLUTION A. 32:44 B. 54:33
Congratulations to Sandeep Bansal, Sriram Bapatla, Aseem Chandawarkar, Shailesh Goregaokar, Nikita Jain, Pankaj Jain, Raghuram Manickam, Roopesh Mathur, Madhavi, Kavitha and Anushya Muralidharan, Bipin Parekh, H. Pillai, Abhijit Shinde and Sahil Somji, who were winners of the last set of puzzles.

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