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For The Mathematically Inclined

Anil Saigal
03/20/2006

FOR CHILDREN

PROBLEM # 1
A digital watch displays hours and minutes with AM and PM. What is the largest possible sum of the digits in the display?

FOR GROWNUPS

PROBLEM # 2
A circle of radius 'r' is concentric with and outside a regular hexagon of side length 2. The probability that three entire sides of the hexagon are visible from a randomly chosen point on the circle is 0.5. What is 'r'?

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-032306 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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SOLUTIONS TO PROBLEMS ON 03/09/06

FOR CHILDREN

PROBLEM # 1
The Math Team in Addville traveled to Subtractville for a math competition.  The bus averaged 40 mph from Addville to Subtractville but averaged 60 mph during the return trip.  What was the average speed of the bus for the entire trip?

SOLUTION
48 mph.

FOR GROWNUPS

PROBLEM # 2
Find the integral of the function sqrt(1 + 1/(x^2/3)) from 0 to 8.

SOLUTION
Sqrt(125) - 1.

Congratulations to Sameera Ayyagary, Virinchi Balabhadraputrani, Sandeep Bansal, Aseem Chandawarkar, Samik Chattopadhyay, Somnath Chattopadhyay, Dattatrya Joshi, Kavitha Muralidharan, Madhavi Muralidharan, Sarthak Pani, Suryateja Rao, Ashvin Sangoram and Ramya Tamisetti, who were winners of the last set of puzzles.



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