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For The Mathematically Inclined

Anil Saigal
10/09/2013

PROBLEM #1


If it takes Bill 20 hours to paint a house and it takes George 30 hours, how long will it take if they work together yet independently?

PROBLEM #2
A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads?

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Please send your solutions to mr.asaigal@gmail.com.

Use Problem Solutions M-101013 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 09/26/13

PROBLEM #1
If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid , combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of 1.

SOLUTION 1
 

PROBLEM #2
A town consists of only one street in the form of a circle. The town authorities give out four licenses for a particular kind of business. The inhabitants of the town live in equal density along the circle and will always go to the closest business for what they need. Business A gets to choose a location first, then business B, then C, and finally D. Each business desires to carve out as much business for themselves as possible but each knows the others all have the same motive. Assume that if a business is indifferent between locating in two different sections of the circle it will choose a section at random. Also assume that the business that goes last will choose a location in the middle of the largest (or one of the largest) sections. Where should business B choose relative to the location of A?

SOLUTION 2



Congratulations to Saba Lateef, who was the winner of the last set of puzzles.



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