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For The Mathematically Inclined

Anil Saigal
04/28/2009


PROBLEM # 1
The first three terms of an arithmetic sequence are 2x-3, 5x-11 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?

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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.



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