Archives
Contribute

For The Mathematically Inclined


Anil Saigal 04/28/2009
PROBLEM # 1 The first three terms of an arithmetic sequence are 2x3, 5x11 and 3x+1, respectively. The nth term of the sequence is 2009. What is n?
PROBLEM #2 Let a + a x + a x^2 + a x^3 + .... and a + a y + a y^2 + a y^3 + .... be two different infinite geometric series of positive numbers with the same first term. The sum of the first series is x, and the sum of the second series is y. What is x+y?
 Please send your solutions to anil@lokvani.com.
Use Problem Solutions M043009 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 Solutions 04/16/09
PROBLEM # 1 Any given length of highway is equally likely to have as many potholes as any other length of equal size. The average number of potholes per mile of highway is 3. What is the probability that 2 miles of highway have 3 or fewer potholes? Solution: P(0)+P(1)+P(2)+P(3) using Poisson's Distribution and mean of 6.
PROBLEM #2 Three people (A, B, and C) need to cross a bridge. A can cross the bridge in 10 minutes, B can cross in 5 minutes, and C can cross in 2 minutes. There is also a bicycle available and any person can cross the bridge in 1 minute with the bicycle. What is the shortest time that all men can get across the bridge? Each man travels at his own constant rate Solution: 5 minutes. Congratulations to Suhas Joglekar and Muneeba Syed, who were the winner of the last set of puzzles.

Share your Comments
In this Issue
Rajyogini Dadi Janki To Speak On Immortality 
Rajyogini Dadi Janki to Speak on Immortality on Thursday, May 7th from 6:30 to 9:00 pm at Back Bay Events Center in Boston. [more]
 
Taruna Garg Named 2009 Heroine 
Massachusetts Commission on the Status of Women announces Taruna Garg of Murtha Cullina LLP as an unsung heroine of 2009.
[more]
 
Oriya Language And Literature 
"Oriya literature encompasses several strains of thought, including Buddhist, Jaina, Sakta, Vaishnava and Vedic," said Dr. Bijoya Misra, as part of the presentation on Oriya Language and Literature on April 11, 2009. [more]
 
It's IPL season so it is time to laugh for cricket! [more]
 
Yadoon Ki Baraat: Smashing Success 
Aaroh's musical evening played to a full house at Keefe Tech in Framingham had the audience rocking to their tunes. Alankar Decors classy backdrop, great dancing by local teenagers and Aloks fashion show made for a great event with all funds raised going to Ekal Vidyalaya. [more]
 
You may also access this article through our website http://www.lokvani.com/

