For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
11/01/2006

FOR CHILDREN

PROBLEM # 1
Radha and Sudha are saving for college. Radha starts with $a in her piggy bank and Sudha starts with $b in hers. Each week, Radha deposits $5 into her piggy bank and Sudha deposits $7 in hers. In 15 weeks, they will have the same amount. In 30 weeks, the ratio of Sudha's savings to Radha's is 8:7. Determine a+b.

FOR GROWNUPS

PROBLEM # 2
A and B got into a fight. The probability that they will see each other on the nth day from now is 3/(3n+5). What is the probability that they will not see each other for the next 31 days.

-------------------------------------------------------------------------------------------------------------

Please send your solutions to anil@lokvani.com.

Use Problem Solutions M-110206 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.

-------------------------------------------------------------------------------------------------------------

SOLUTIONS TO PROBLEMS ON 10/19/06

FOR CHILDREN

PROBLEM # 1
From a book, a number of consecutive pages are missing. The sum of the page numbers of these pages is 9808.

The Question: Which pages are missing?

SOLUTION
291 - 322.

FOR GROWNUPS

PROBLEM # 2
Long ago, a young prince wanted to marry a King's daughter. The King decided to test the prince. He gave the prince two empty, porcelain vases, 100 white pearls, and 100 black pearls. "You must put all the pearls in the vases", he told the prince. "After this, I will call my daughter from the room next door. She will take a random pearl from one of the two vases. If this pearl is a black one, you are allowed to marry my daughter."

The Question: What was the best way in which the prince could divide the pearls over the vases?

SOLUTION
One black pearl in one vase and the remaining 199 pearls in the other vase.

Congratulations to Ruby Bansal, Sandeep Bansal, Anindaya Basu, Suhas Joglekar, Dattatraya Joshi, Mukkai Krishnamoorthy, Samir Mehta, Samita Mohan, Indira Nouduri and Ranga Raghupati, who were winners of the last set of puzzles.

You may also access this article through our web-site http://www.lokvani.com/