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For The Mathematically Inclined

Anil Saigal
01/14/2004

FOR CHILDREN

PROBLEM # 1

Tommy has a 1.69 ounce bag of M&Ms. The bag contains 56 M&Ms. He decides to share his candy by giving Lucy two-thirds of three-fourths of his M&Ms. Lucy decides to share her M&Ms with Melissa by giving Melissa two-thirds of three-fourths of her M&Ms. If half of Melissa's M&Ms are red, how many red M&Ms does she have?

PROBLEM # 2

DOGSANDCATSDOGSANDCATSDOGSANDCATS…..

If the above pattern continues, what will be the 101st letter in the pattern?

FOR GROWNUPS

PROBLEM # 3
How many people must be at a party before you have even odds or better (probability that birthday of two people is on same day >= 0.5) of two having the same bithday (not necessarily the same year, of course)?

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Please send your solutions to anil@lokvani.com.

Use "Problem Solutions M-011504" as the subject line. Please include your full name in the text of the main message. The first one to submit the right answer will be profiled in the next issue of Lokvani.

Please do not post your solution in "Post Comments". No credit will be give for solutions not sent to anil@lokvani.com.

If you need clarification on any problem, please contact anil@lokvani.com.

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SOLUTIONS TO PROBLEMS ON 01/01/04

PROBLEM # 1

1,2,4,8,...

SOLUTION

1,2,4,8,16,32,64,128,...
This is sequence of sum of Binomial co-efficients.

PROBLEM # 2

1,1,2,3,.....

SOLUTION

1,1,2,3,5,8,11,19,...
This is the series of Fibonacci Numbers.

PROBLEM # 3
1,5, 61,1385,.....

SOLUTION

1,5, 61, 1385, 50261, 2702765, 199360981, 19391512145, …
It is the sequence of Euler numbers.

WINNERS

Congratulations to Rahul Banerjee, Deepa Santhumayor, Mukund Seshadri and Sumanth Shankar who were winners of the last set of puzzles.



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