The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from

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## The Coin Toss Puzzle and the Simplest Possible Solution

Recently, I wrote an article on why the Monty Hall problem has perplexed so many brilliant minds where I showed that it was a corner case between 1 open and 1 closed door, while the intuitive but wrong answer is close to the probability curve of 1 open door. Now a coin toss puzzle has appeared on Twitter [1] that has gone viral as it goes against our common intuition of probability and random sequences (such as a series of coin tosses). The puzzle goes as follows. The Problem Flip a fair coin 100 times—it gives a sequence of heads

Continue reading## DSP and the Humand Mind

It is relatively straightforward to establish the power and potential of human organs. The results are deterministic and not much different than animals. For example, my arm or leg can move only within a certain range and perform a limited number of known tasks. On the other hand, the possibilities with the mind are unlimited. For example, it can plan and execute a drilling mission to dig tunnels in the moons Titan and Europa, all the while sitting here on planet earth! We can say that the mind is the most mysterious organ not only in the human body but

Continue reading## CDMA or OFDM

Reading about interference cancellation techniques today, I recalled an interesting article by Sridhar Vembu titled Two Philosophies in CDMA: A Stroll Down Memory Lane. Vembu is the founder and CEO of Zoho Corporation, a venture which has turned him into a billionaire. He spent time both in academia (at Princeton) and in industry (at Qualcomm) working with the likes of Sergio Verdu in one camp and Andrew Viterbi in the other. Here are some excerpts from his article which is not available online anymore at the time of this writing. I have now worked a little over 10 years in

Continue reading## Why the Constant e Arises in Complex Plane as a Rotation

In the tutorial on how complex numbers arose, we asked three questions. The first two were answered in the same article while the answer to the third question, repeated below, is explained here. Why is the expression $e^{i \theta}$ a rotation of 1 by $\theta$ radians on a unit circle? Is it possible to make sense out of a number like $2.71828^{\sqrt{-1}\cdot\theta}$? The constant e is a special number discovered by Jacob Bernoulli while studying compound interests. It appears in many other forms as well which are all related to each other but that topic is a complete account in

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