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For The Mathematically Inclined

Anil Saigal
04/24/2007

FOR CHILDREN

PROBLEM # 1
Lets say you walked all the way across the equator. Assuming that your height is about 6 feet, how much farther would  your head travel than your feet? Give your answer in feet, rounded to the nearest tenth.

FOR GROWNUPS

PROBLEM # 2
Given (see Figure 1):
(sphere) x^2 + y^2 + z^2  = 25
(plane a)   y=2
(point) A (3, 4, 0)
AB=Diameter
AB intersects plane a at M
Find MB:AM.

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Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-050307 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 04/19/07

FOR CHILDREN

PROBLEM # 1
A small store has two full-time employees. If each employee is absent about 3% of the days the store is open, what is the probability that both employees will be absent on the same day!

SOLUTION
0.0009. 

FOR GROWNUPS

PROBLEM # 2
A cyclist drove one kilometer, with the wind in his back, in three minutes and drove the same way back, against the wind in four minutes.

The Question: If we assume that the cyclist always puts constant force on the pedals, how much time would it take him to drive one kilometer without wind?

SOLUTION 
24/7 minutes.

Congratulations to Sandeep Bansal, Shailesh Goregaokar, Dattatraya Joshi and Samir Mehta, who were winners of the last set of puzzles.



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Figure 1

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