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For The Mathematically Inclined

Anil Saigal

Problem 1

A shopkeeper wants to be able to dispense sugar in whole pounds ranging from one pound up to 40 pounds. He has a standard, equal-arm balance weigh scale. Being of an extremely economical outlook, he wants to use the least possible number of weights to enable him to weigh any number of pounds between 1 and 40. How many weights does he need and what are they?

Problem 2
A set of encyclopedias consists of volumes that have 1/8-inch covers and one inch of pages. The set is arranged in order on a shelf from left to right. If a bookworm starts at the first page of Volume I and eats its way through to the last page of Volume II, how far does it travel?


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

Use Problem Solutions M-092515 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. 


Problem #1
A chauffeur always arrives at the train station at exactly five o'clock to pick up his boss and drive her home. One day his boss arrives an hour early, starts walking home, and is picked up by the chauffeur on the way out to the train station. They arrive at home twenty minutes earlier than usual. How long did she walk before she met her chauffeur?

Problem #2

Two boys on bicycles 20 miles apart, began racing directly toward each other. The instance they started, a fly on the handle of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handle bar it turned and started back. The fly went back and forth this way, from handle bar to handle bar, until the two bicycles met.If each bicycle had a constant speed of 10 miles per hour, and the fly flew at a constant speed of 15 miles per hour, how far did the fly fly?

Congratulations to RK Sambangi, who was the winner of last set of puzzles. 

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