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For The Mathematically Inclined

Anil Saigal

The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town


You intend to fly non-stop around the world.  But you can only go halfway around the world on a full tank. However you can arrange many planes exactly like yours to assist with refuelling. Assuming refuelling can be done midair, ignoring refuelling and turning time, and without crashing any plane, what is the minimum number of planes you will need?


Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-030410 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.


Problems from 02/18/10


A farmer has three straight pieces of fencing: 2, 3, and 4 yards in length.  What is the maximum area he can enclose by connecting the pieces?  Assume the land is flat.


2.79 sq. yards.


Find the value of the infinite product

P = 7/9 * 26/28 * 63/65 * ... * (k^3 - 1)/(k^3 + 1) * ...



Congratulations to Sitaram Chandawarkar, who was winners of the last set of puzzles.

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