For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
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PROBLEM #1

One morning is starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?

PROBLEM #2

Given n points drawn randomly on the circumference of a circle, what is the probability they will all be within any common semicircle?

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

Use Problem Solutions M-122012 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 12/06/12

PROBLEM #1

What 5-digit number has the following features:

If we put the numeral 1 at the beginning, we get a number three times smaller than if we put the numeral 1 at the end of the number.

SOLUTION 1
42857.

PROBLEM #2
A pearl necklace has 33 pearls with the largest and most valuable in the middle. Starting from one end, each successive pearl is worth $100 more than the one before (up to the middle one), but starting from the other end each pearl is worth $150 more than the one before, up to the big pearl. The whole necklace is worth $65 000. What is the value of the middle pearl?

SOLUTION 1
$3,000.

Congratulations to Kishore Balsara, Abhimanyu Bhargava, Lalit Doshi, Suhas Joglekar, Prabhakar Nadkarni and Suraj Srinivasan, who were the winners of the last set of puzzles.

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