Homepage of Amitabha Ghosh

"We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on." Richard P. Feynman, Physicist, Noble Laureate.

Amitabha Ghosh

Ph.D. Candidate

Autonomous Networks Research Group
Ming Hsieh Department of Electrical Engineering - Systems
Viterbi School of Engineering
University of Southern California
Los Angeles, CA 90089

Email: amitabhg@usc.edu

Office:

Ronald Tutor Hall (RTH) 419
3710 S. McClintock Avenue
Los Angeles, CA 90089
Ph. (213) 740 3759

Last updated: April 30, 2009.

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Math

The Card Trick:
Consider a deck of 52 cards, lying on a table. Now slide the topmost card forward without moving any of the others cards. The maximum distance you can slide the card forward until it falls is half the card's length. Now push the second card outwards. How much maximum overhang would you get? Well, it's 1/2 + 1/4 = 3/4 of a cards' length. If you continue this opertion with all the remaining cards, how much total overhang would you get with a total of 52 cards?

Gossip:
n people each know a different piece of gossip. They can telephone each other and exchange all the information they know (so that after the call they both know anything that either of them knew before the call). What is the smallest number of calls needed so that everyone knows everything?

Tower:
R = N^(N^(N^...)). What is the maximum N>0 that will yield a finite R?

Rubberband:
A bug walks down a rubber band which is attached to a wall at one end and a car moving away from the wall at the other end. The car is moving at 1 m/sec while the bug is only moving at 1 cm/sec. Assuming the rubber band is uniformly and infinitely elastic, will the bug ever reach the car?