Almost three weeks gone on the Chandrayaan Engine Room puzzle (Puzzle 2), and we are getting to ready to close it down. We are planning to keep it live for another couple of days. For those sticking on till the end, here is a hint : think about lighting one of the wires on both ends.

In the meantime, here is a clip from the show "Golden Balls." "Golden Balls" runs a version of Prisoner's Dilemma as part of the show. In this show, they had a hundred thousand pounds on offer. Enjoy!

## Note to recruiters

Note to recruiters:
We are quite aware that recruiters, interviewers, VCs and other professionals generally perform a Google Search before they interview someone, take a pitch from someone, et cetera. Please keep in mind that not everything put on the Internet must align directly to one's future career and/or one's future product portfolio. Sometimes, people do put things on the Internet just because. Just because. It may be out of their personal interests, which may have nothing to do with their professional interests. Or it may be for some other reason. Recruiters seem to have this wrong-headed notion that if somebody is not signalling their interests in a certain area online, then that means that they are not interested in that area at all. It is worth pointing out that economics pretty much underlies the areas of marketing, strategy, operations and finance. And this blog is about economics. With metta, let us. by all means, be reflective about this whole business of business. Also, see our post on "The Multi-faceted Identity Problem".

## Sunday, April 29, 2012

## Saturday, April 21, 2012

### Pictures from Thailand

I promised Prof. Shankar that I would post some pictures of Thailand on the blog. And here is a first set of pictures. The pictures are from the Suvarnabhumi airport in Bangkok, and these pictures depict the churning of the mythic ocean from Hindu mythology.

## Friday, April 13, 2012

### Einsteinian relativity, Milton Friedman, Steven Pinker, the Socratic method et cetera

I would like to make a few additional points regarding the wires puzzle (a.k.a. the Chandrayaan Engine Room puzzle) in the column, and then switch over to some thoughts from an organizational perspective. The wires puzzle is an old one. There are versions of it all over the Internet. What is different here is the use of the Chandrayaan theme. Since this is happening aboard Chandrayaan, there could be relativistic effects that may need to be considered. The point of posting this puzzle using the Chandrayaan theme is to say that, sometimes, old problems can be looked at in new ways.

That is, one interesting way to think about the problem is to ask if the solution to the problem changes if we have relativistic effects. If the rate at which the wires burn changes over time, then you suddenly have a more interesting problem. The point is that if we shift the 'frame' of the problem, then sometimes, the problem itself changes. (See Steven Pinker's discussion of some of these 'framing' effects in Chapter 5 of his book "How the Mind Works".)

We are planning on a puzzle in Finance in a future column. With Finance problems, there may be other assumptions such as time preference of money. Milton Friedman talked about problems and assumptions in his famous paper "The Methodology of Positive Economics". As Friedman put it, theories almost always make assumptions, and so the solving of a puzzle is a Socratic process in that the framer of the problem and the anwerer must agree on a certain set of assumptions. But beyond agreeing on the set of assumptions, nothing more is required.

Now, puzzles are often used in interviews, and one person even termed his interviewing process Socratic. I do not think, however, that a Socratic approach to puzzles is a good one. It seems to be a rather mistaken approach. From what I have seen, the dialogue that ensues after a puzzle is proposed is almost never about clarifying assumptions behind the problem. The dialogue is about the interviewer providing the interviewee subtle clues to solving it. How many clues the interviewer provides the interviewee depends on how much the interviewer likes the interviewee at first blush. And that's not ideal if we want the organization to pick the best people since first impressions can often be mistaken. There is a problem here that I am calling your attention to and it is an organizational one. Most interview puzzles are quite sufficiently specified, and so the requirement these days that interviewers engage in a dialogue with the interviewee seems rather wrong headed. It ought to be sufficient for the interviewer

**to clarify assumptions**underlying puzzles, and then let the interviewee figure out the rest on his or her own.

The whole point of puzzles is to have an objective means of analyzing candidates. There is much subjectivity in almost every other part of the process. Companies really ought to change the way they interview candidates. Why companies continue to do interviews they way they do is, of course, a whole different ball of wax.

**This is a very technical post. You can safely skip this post and still enjoy the puzzles in this column. You can also assume that there are no relativity effects in coming up with a solution.**

__Update (June 18):__## Thursday, April 12, 2012

### The two wires puzzle a.k.a. the Chandrayaan engine room puzzle

A friend of mine had a question on this month's main puzzle, and so I would like to make one clarification regarding the two wires puzzle. The rate of burning of the two wires may be termed as "fixed but unknown". The first wire may burn as follows : 1 minute for the first 1%, another 2 minutes for the next 1 % and so on. At the end of 10 minutes, only 9% of the wire may have burned. However, since each wire takes an hour to burn through, the rest of the 91% of the first wire will burn in the next 50 minutes. The wire may be burned from either end. Similarly for the second wire.

Note that the way that the second wire burns may not be the same as the way that the first wire burns. Thus, the second wire may burn as follows : 2 minutes for the first 1%, 4 minutes for the next 1% and so on. At the end of 10 minutes, only 3% of the wire may have burned. But since the wire takes an hour to burn through, the rest of the 97% of the second wire would burn in the next 50 minutes. I use the term "fixed but unknown" because while the way the two wires burn is not known, the way the two wires burn does not change over the period of time in question.

Note that the way that the second wire burns may not be the same as the way that the first wire burns. Thus, the second wire may burn as follows : 2 minutes for the first 1%, 4 minutes for the next 1% and so on. At the end of 10 minutes, only 3% of the wire may have burned. But since the wire takes an hour to burn through, the rest of the 97% of the second wire would burn in the next 50 minutes. I use the term "fixed but unknown" because while the way the two wires burn is not known, the way the two wires burn does not change over the period of time in question.

(Chandrayaan Engine Room)Chandrayaan-12 has run into trouble. The problem is in the engine room, and the initial investigation into the problem has revealed that the positron motor needs to be restarted. This needs to be done exactly 45 minutes after the neutrino drive is turned off. However, the clocks in Chandrayaan are no longer reliable. All you have are two wires. The two wires each take exactly an hour to burn. They don't burn uniformly, however. So, for instance, the first half of the first wire may take 13 minutes to burn and the second half 47 minutes. Is it possible to measure out exactly 45 minutes using the two wires? If so, how?

**Mathematically speaking, let the length of the first wire that burns in time t be f1(t). This function is not known. It could be of the form [ f1(t) = k.t ], but it could be quite different as well. You don't need to understand any advanced mathematics to solve the problem, however, and for this reason, we have avoided using mathematical notation for the problem.**__Update:__## Tuesday, April 10, 2012

### Inequality of the means

*To skip the talk and go straight to the this month's main puzzle, just go to the Indiatimes article (linked here) and scroll all the way down.*

Indiatimes is running an edited version of this article, which is the next installment of the puzzle column. This article is in collaboration with Prof. Krishnan Shankar of the University of Oklahoma.

The main problem in this article, the geometric version of the Inequality of the Means, has been chosen for its simplicity and elegance. It is one of those mathematical problems that is easy to state but ridiculously hard to prove. There are two puzzles this month. Please be sure to use the two different Subject lines mentioned in the article to help us distinguish which puzzle it is you are replying to.

A note regarding the "New Dice" puzzle - the problem is not asking whether it is possible to number the dice such that each possible outcome 2 through 12 occurs with equal probability. The problem is to come up with numbers a1, a2, a3, a4, a5 and a6 for one dice and b1, b2, b3, b4, b5 and b6 for the second dice (together, a1 through a6 and b1 through b6 form a "numbering") such that the following properties are satisfied:

- Together, a1 through a6 and b1 through b6 constitute two sets of 1 through 6.
- The "numbering" is not identical to the default "numbering".
- The "numbering" would lead to the same probability distribution of outcomes as the 1,2,3,4,5,6; 1,2,3,4,5,6 numbering.

INEQUALITY OF THE MEANS

This article is in collaboration with Prof. Krishnan Shankar, Professor of Mathematics at the University of Oklahoma.

The Oracle Asks

This article’s material came forth from the fertile mind of the extraordinary John Conway. References to the mathematics of the problem are listed at the end. It was a pleasure to discuss this problem with Prof. Dror Bar-Natan. Prof. Bar-Natan’s exposition and Javascript applet make the subject come alive on his website (http://www.math.toronto.edu/~drorbn/), which is certainly worth a visit.

We start with a well-known inequality from high school algebra: let a and b be any two non-negative numbers. Then, their arithmetic mean is at least as large as their geometric mean, i.e.,

square_root(a *b ) <= ((a + b)/2)

Equality occurs precisely when a = b. This is not hard to prove algebraically, but here is a nice geometric proof. Consider the following figure where a square of side length a + b encloses 8 right angled triangles of orthogonal sides a and b each.

## Saturday, April 7, 2012

### Oklahoma Sooners

We have written up columns for the next few months, and will be proof reading them and preparing them for publication over the next few weeks. We will get it all done real soon. For the summer, we are planning to have three short columns, ones that will mainly consist of just the puzzle itself. The first summer puzzle has a beach theme, and the second one a game theme. The third is still work in progress.

While we are on the topic of games, it would be good to say a little something about Oklahoma Sooner football and even American football games in general. A football game in Norman or Austin is much more than a game. It is a celebration. The long running rivalry between the University of Oklahoma-Norman and the University of Nebraska-Lincoln no longer exists, since it has now been replaced with the Red River Rivalry, but when it was around, it was one for the ages. Here is a clip from a 1986 game.

Even people from Europe typically don't realize how big these football games are as events. A game between these two teams from relatively small towns, Lincoln and Norman, the former with a population of about 250,000 and the latter with about 100,000, is quite a spectacle even on TV. Being a part of the spectacle was eye opening for me when I was in America fresh from India. To me, it was proof of the robustness of the American economy that these relatively small towns are able to stage high attendance games through the football season and yet have all the pomp and pageantry that you might only expect to find in games having large metropolitan area audiences. The rivalry game is often the most closely fought one in the football season, and all the big universities have a rivalry game. In the big rivalry game, the wins are to be cherished and celebrated and the losses are never to be forgotten, decades to come. You really have to see it to believe it.

While we are on the topic of games, it would be good to say a little something about Oklahoma Sooner football and even American football games in general. A football game in Norman or Austin is much more than a game. It is a celebration. The long running rivalry between the University of Oklahoma-Norman and the University of Nebraska-Lincoln no longer exists, since it has now been replaced with the Red River Rivalry, but when it was around, it was one for the ages. Here is a clip from a 1986 game.

Subscribe to:
Posts (Atom)