problem-solving on S Anand

White Pebble Black Pebble

Wed, 04 Mar 2026 22:23:29 +0800

When I was in class 8 or 9, our English teacher told us a story I’ll never forget.

There was a poor farmer who lived in a village. He owed the zamindar (landlord) of the village a lot of money.

The zamindar had an eye on his daughter. “Marry your daughter to me, and I’ll forgive your debt,” he said.

The farmer was reluctant. “Please, sir, what will the village say about your marrying such a young girl?” he asked.

The wily zamindar said, “They cannot argue with God’s will. Let fate decide.”

The zamindar gathered the villagers near the river, picked up pebbles of white and black from the riverbed, and told the farmer, “I will put a white and black pebble in this bag. If your daughter picks the black pebble, fate wills that she marry me. If she picks the white pebble, she needn’t. Your debt will be forgiven.”

But without the villager’s knowledge, the zamindar put two black pebbles in the bag.

The farmer’s daughter saw this, and was in a dilemma. Exposing the zamindar force them back into debt.

Instead, she picked a pebble from the bag dropped it “by accident” among other pebbles. “Sorry!” she said. “But let me see which pebble is left in the bag.”

She showed the remaining black pebble from the bag. “I must have picked the white. Fate forgives our debt without marriage, sir.”

I remember this story is because it converts a “no-win” situation into a “no-lose” one – just by reframing the problem.

Whenever I think, “Damn! What a mess!” I hope I have enough wits to remember this story. There are many more black-pebble problems in life than we realize. We just need to be creative enough to drop the pebble and reframe the problem.

Why don't students hack exams when they can?

Fri, 22 Nov 2024 10:38:09 +0000

This year, I created a series of tests for my course at IITM and to recruit for Gramener.

The tests had 2 interesting features.

One question required them to hack the page

Write the body of the request to an OpenAI chat completion call that:

Uses model gpt-4o-mini

Has a system message: Respond in JSON

Has a user message: Generate 10 random addresses in the US

Uses structured outputs to respond with an object addresses which is an array of objects with required fields: street (string) city (string) apartment (string) .

Sets additionalProperties to false to prevent additional properties.

What is the JSON body we should send to https://api.openai.com/v1/chat/completions for this? (No need to run it or to use an API key. Just write the body of the request below.)

There's no answer box above. Figure out how to enable it. That's part of the test.

The only way to even attempt this question is to inspect the page, find the hidden input and make it visible. (This requires removing a class, an attribute, and a style - from different places.)

Here's the number of people who managed to enable the text box and answer it.

College	# students	Enabled	Answered
NIT Bhopal	144	4 (2.8%)	0 (0.0%)
CBIT	277	16 (5.8%)	0 (0.0%)
IIT Madras	693	74 (10.7%)	4 (0.6%)

A few things surprised me.

First, I think students don't inspect HTML. Less than 10% of students managed to modify the HTML page, even after being told they need to. But they know web programming. 49 students at CBIT scored full marks on the rest of the questions, which includes CSS selectors and complex JS code. Maybe editing in a browser instead of an editor is a big mental leap?

Second, almost no one could solve this problem. There are 3 ways to easily solve it.

Copy the question and relevant test cases from my exam page's JavaScript into ChatGPT and ask for an answer. (I test it and it works.)
Copy the question and structured output documentation to ChatGPT and ask for an answer. (I tested it and it works.)
Create a random JSON and just keep fixing the errors manually until it passes. (The exam gives detailed error messages like "The system message must be 'Respond in JSON'", "addresses items must be an object", etc.)

Maybe questions from a curriculum are easier to solve than questions not in a curriculum? Or is JSON schema too hard?

The exam was officially hackable

All validation was on the client side. The JS code was minified and answers are dynamically generated. But a student can set a breakpoint, see the answers, and modify their responses.

The students at NIT Bhopal and CBIT were not explicitly told that. The students at IITM were explicitly told that they could (and are welcome to) hack it.

Out of the 1,114 students who took these tests, only one student actually hacked it.

(How do I know that? No other student got full marks. This student got full marks with empty answers.)

It's probably not that difficult. My course content covers scraping pages using JavaScript using DevTools. Inspecting JS is just a step away.

I did chat with the student who hacked it, asking:

Anand: How come you didn't share the details of the hack with others?

Student: I did with a few but I am not sure whether or not they were able to figure it out still.
Most students in the program still require a lot of handholding even with basic things.
Experience from being a TA [Teaching Assistant] past term.

Why didn't they hack?

Maybe...

They don't believe me. What if hacking the exam page is considered cheating, even if explicitly allowed?
The time pressure is too much. They'd rather solve what they know than risk wasting time hacking.
It feels wrong. They'd rather answer based on their knowledge than take a shortcut.
They don't know how. Using DevTools is more sophisticated than web programming.

Issue #1 - the trust issue - is solveable. We can issue multiple official notices.

Issue #4 - capability - is not worth solving. My aim is to get students to do stuff they weren't taught.

Issue #2 & #3 - a risk-taking culture - is what I want to encourage. It might teach them to blur ethical lines and neglect fundamentals (which are bad), but it might also build adaptability, creativity, and prepare them for real-world scenarios.

Personally, I need more team members that get the job done even if they've never done it before.

How to extend Markdown with custom blocks

Fri, 08 Jan 2021 09:37:48 +0000

One problem I’ve had in Markdown is rendering a content in columns.

On Bootstrap, the markup would look like this:

<div class="row">
  <div class="col">...</div>
  <div class="col">...</div>
</div>

How do we get that into Markdown without writing HTML?

On Python, the attribute lists extension lets you add a class. For example:

This is some content
{: .row}

… renders <p class="row">This is some content</p>.

But I can’t do that to multiple paragraphs. Nor can I next content, i.e. add a .col inside the .row.

Enter markdown-customblocks. It’s a Python module that extends Python Markdown. This lets me write:

::: row
::: col
Content in column 1
::: col
Content in column 2
::: row
::: col
Content in column 1
::: col
Content in column 2

This translates to:

<div class="row">
  <div class="col">Content in column 1</div>
  <div class="col">Content in column 2</div>
</div>

Better yet, we can create our own custom HTML block types. For example, this code:

from markdown import Markdown
from customblocks import CustomBlocksExtension

def audio(ctx, src, type="audio/mp3"):
    return f'''<audio src="{src}" type="{type}">
      {ctx.content}
    </audio>'''

md = Markdown(extensions=[
    CustomBlocksExtension(generators={
        'audio': audio
    }),
])

… lets you convert this piece of Markdown:

md.convert("""
::: audio src="mymusic.ogg" type="audio/ogg"
    Your browser does not support `audio`.
""")

… into this HTML:

<audio src="mymusic.ogg" type="audio/ogg">
  Your browser does not support <code>audio</code>.
</audio>

markdown-customblocks is easily the most useful Python module I discovered last quarter.

Implicit information

Thu, 03 Jan 2008 12:00:00 +0000

From what I’ve seen, puzzles and exam questions share two un-real-worldly characteristics. Firstly, you are guaranteed that a solution exists. Secondly, you are given that all the information provided to you is relevant. (Well, not always. Some case studies I’ve seen have had their share of contrived irrelevance. But that’s often what it is, I think. People fill in the relevant stuff, and then try and distract by adding irrelevant material in the hope of making it more real-world-like. But that’s just a guess).

These are very powerful constraints. I know of nothing that has given me as much confidence in solving puzzles as the assurance that a solution exists (and that someone thinks me capable of getting it).

But it’s more than just a confidence builder. The guarantee that a solution (and invariably it’s a unique) is a very powerful one. An extreme case is an objective type question, which explicitly provides three guarantees:

There is a solution
There is only ONE solution
It is among the choices listed below

(Some papers try and take away the first guarantee by having an (E) None of the above category. But that’s still leaving behind the other two more powerful guarantees.)

Marking answers randomly, or marking (A) for every question would still get you 25% in an exam with 4 choices. (Marking (C) would prove just as good, unless you had a kind professor like this.) That’s better than any real-world scenario I’ve seen. (Real-world strategies aren’t much better, though.)

Using guarantee 2, you can eliminate choices easily. If (A) and (B) do not satisfy some property of the solution, they CANNOT be the answer. There’s only one solution, and these are not it.

Using guarantee 3, you can pick the last remaining choice wihout having to check it. The solution is definitely among the choices listed. So you don’t need to solve an objective type question. You just need to pick the right answer – which is completely different.

The principle applies even outside of objective type questions, especially in mathematically-oriented problems, or puzzles. And you can solve it by trial and error. For example, try this one from Martin Gardner’s Mathematical Magic Show:

Two brothers own n sheep, each of which is sold for n dollars. Thus they have n2 dollars in all. This is in the form of 10 dollar notes and 1 dollar coins, the number of 1 dollar coins being less than 10 dollars. The elder brother divides the money as follows: he takes a note for himself, gives one to his younger brother, takes a note for himself and so on. At the end, the younger brother complains that the elder took the first note as well as the last. So the elder gives the younger all the one dollar coins. The younger brother complains that he still has more. So the elder brother writes the younger a cheque to equalize their share. What was the cheque for?

Now, this is a weird problem. Think about it. You’re told almost NOTHING. And you have to guess what the amount is. (Note: you don’t have to guess what ’n’ is. That’s impossible.)

Here’s how I solved the problem. I said, let me find even one case where the elder brother gets the first and last note. Let’s see what the answer is. Whatever the answer is for that case, it has to be the answer for all other cases – because otherwise, the problem does not have a unique solution.

So I tried n=1. n=2. n=3. For n=4, the amount is 16. That’s 1 $10 note and 6 $1 coins. The elder brother would get the first and the last $10 note. The younger would get $6. So the elder would have $4 more than the younger, and would write out a cheque for $2. (It’s amazing how many people get as far as the $4, but forget to divide by two.)

You can try if for any other value that has an odd number of $10 notes. It has to be for n ending with 4 or 6. That means n2 ends in 6, and the cheque has to be for $2.

Notice that you didn’t need number theory to get the answer. The assurance that there is a unique answer is enough.

There’s another kind of implicit information usually available: the amount of information there is. For example, take the following question:

Which city has a higher population: San Antonio or San Diego?

Children in the US apparantly had difficulty answering it. Children in Germany had less trouble. The reason? The German kids had heard of San Diego, but not San Antonio. They figured the one they’d heard of was more likely bigger. Knowing less may be better.

It’s the same principle you use to check spellings. Run a Google search on two spellings. The one that returns a higher number of results is the correct spelling. (Of course, Google has a spelling correction mechanism that works well, but I use it for Tamil words. I can never tell if I should use ர or ற.)

Of course, the fundamental assumption here is: MORE INFORMATION = MORE CORRECT, which is not always the case. But the point I’m driving to is this:

You’re always given additional information. Even if you’re not given any information, that’s informative.

Comments

Sathyaraj 3 Jan 2008 12:00 pm: this article was “fucking” good..i was reading a book called fooled by randomness and i just could relate to the way you and the author went about writing this.. can you write more about monte carlo simulation too?? and how it is used in finance…
Vasanth 3 Jan 2008 12:00 pm: Very interesting post! New insight for me into puzzles. I had always realized, but never analyzed, that I never give up when it comes to puzzles and brain teasers. On the contrary I give up relatively easily with some technical or work related problem the minute it appears probable that a (reasonable) solution does not exist.
S Anand 3 Jan 2008 12:00 pm: @Sathyaraj: Thanks! The sequel to “Fooled by Randomness” is pretty good to: “The Black Swan”. @Vasanth: Another big problem, if you ask me, is that the problem is unbounded. In puzzles, you have a test case to determine whether you’ve solved it or not. In life, you aren’t often sure.
Jayanth Sankar 3 Jan 2008 12:00 pm: Hey I like your posts. Pretty good. The question about the money between the two brothers.. I have a doubt here.. you had mentioned number of 1 dollar notes should be less than 10 dollar notes, so then 16 wont work right ? 1 - $ 10 and 6 - $1… what am I missing ?

Solving multiple choice questions

Fri, 19 Jan 2007 12:00:00 +0000

How would you solve this multiple-choice problem: What is 12345 x 45678?

201932843
563894910
402394820
384718349
938491834

It always amazes me when people try and multiply the two numbers. In any objective-type test (multiple choice question), the aim is not to solve the problem – it is to pick the correct answer!

Most people don’t seem to realise the difference.

If I had to solve the problem, I’d look for shortcuts. For example,

All answers have 9 digits. So that’s not going to help.
12345 ends with a 5. All multiples of 5 end with 5. So the answer is either (2) or (3).
1. ~~201932843~~
2. 563894910
3. 402394820
4. ~~384718349~~
5. ~~938491834~~
Multiplying the first digits, 1 X 4 = 4. So the answer’s got to start with a bit more than 4. (3) starts with 40. That’s too low. C’mon, the second number STARTS with 45. So… 2. 563894910 3. ~~402394820~~

This takes me 10 seconds. Multiplying the two takes me ten times as long.

Let me repeat the point: You DON’T have to get to the answer. You’ve already been given the answer. You just don’t know which one it is. And you don’t have to solve the entire problem to pick the right one.

There are many ways of picking the right answer. One is what I just used: the answer must satisfy some property. In this case, the answer must be a multiple of 5.

In other cases, the answer must be close to something. For example, what’s 37463 x 28438?

532686397
1065372794
2130745588
4261491176
8522982352

Well, let’s just multiply the first two digits: 37 x 28. That’s 1036. So the answer’s got to be close. OK, (2) is the answer.

These are not one-off techniques, nor are these applicable only to numbers. You can always pick the right choice without solving the problem.

A weaker, but more general version of the above rule is: you can always eliminate choices without solving the problem.

I’ll blog more on this shortly.

Comments

anand 19 Jan 2007 9:47 am: hats off. U made me to think…….
Vinodh 19 Jan 2007 11:16 am: First rule should be to eliminate the options based on the product of the last digits. So, for the second example, it’s easier to eliminate all the other four options based on this rule. Of course, there are easier techniques for generic multiplication/division as well…I have an somewhat interesting technique to calculate squares/products based on simple algebraic formulae…of course they are better used with some practice, but very powerful.
jake 19 Jan 2007 1:44 pm: its easier and faster to get the answer for the second one by looking at the last digit of the answers. it has to be the same as the last digit of the product of the unit place digits of the numbers being multiplied.
Shreyas 20 Jan 2007 8:14 am: “All multiples of 5 end with 5” - I guess it should be “All multiples of 5 end with 5 or 0” :)
Anonymous 20 Jan 2007 7:55 pm: CAN YOU PLEASE TELL ME WHERE i CAN FIND MORE TIPS ON SOLVING MCQ? I LIKED GOING THROUH THIS BUT I NEED MORE PRACTICE. THANK YOU
Anonymous 22 Jan 2007 5:58 pm: There is a much better way to solve Q2. the last digit of N1 is 3 and the last digit of N2 is 8. 3*8 is 24 so N1*N2 has to end with 4. so the answer should be
GV Rao 7 Mar 2007 7:42 am: I would like to multiply first 2 digits: 45 x 78, and in second case: 3 x 8, which is easy, last digits gives more guess on product.
Sri Lankan Friends 10 Mar 2007 10:23 am: hmmm very interesting
ali 24 May 2007 8:16 pm: good but should be more efficent via understanding
vasudha 19 Jan 2007 12:00 pm: HATS OFF TO YOU… THE INFORMATION IS PRETTY GOOD.. YOU MADE ME THINK
deepak 25 Feb 2011 6:20 am: phaltu trick sab hai… issss se kahi behtar tricks mere paas hai…. sirf tukka maar ke IIT me aa gaya hu YES I AM IN IIT…

Absolutely convergent series

Thu, 31 Aug 2006 12:00:00 +0000

I’ve seen many proofs that 1=2. Here’s a classic.

The (not-so-subtle) error in the above proof is that we’re cancelling (a-b) on both sides, when (a-b) equals zero. That is, we’re dividing by zero on both sides. That completely invalidates the equality.

Another proof uses the fact that the square root of a number can be both positive or negative.

(Proving -1=1 is the same as proving 1=2. Once you have one wrong proof, you can prove every other falsehood.)

The flaw here is that the square root of 1 is 1 and -1. So right after the square root symbol appears, every equation should have a plus-or-minus symbol on both sides.

The most convincing proof uses absolutely convergent series as the key idea. Here’s how the proof goes.

Most people initially think that the flaw is in the re-arrangement of the series. That’s not true! The re-arrangement works just fine, and you can prove that every term is correct to infinity.

The flaw is subtler.

When an infinite series is summed, it can be summed in any order. But the total may vary depending on the order you sum it up! You are guaranteed that the total is the same only if the series is absolutely convergent. That is, if the sum of the absolute values of each number is finite. (See the Wikipedia article on the Riemann series theorem.)

For the log 2 series, it’s not absolutely convergent. The series diverges, as shown below:

So, by re-arranging the series for log 2, we’ve invalidated the equality anyway.

This fact once saved an entire class. We had a problem in our first year physics course to which the answer was the series above. (It had to do with calculating the electromagnetic potential created by an array of charges.) Since the series is not absolutely convergent, and every possible answer was correct, the whole class got marks for this question, as long as they attempted it.

Comments

Arun 1 Sep 2006 1:18 pm: hi da how much u analyze and write amazing i read ur blog continuously for the past four years keep blogging interesting
S Anand 1 Sep 2006 5:28 pm: Thanks! It’s tough to manage, but nowadays I have a lot more time than I used to.
saurabh 2 Apr 2007 7:28 am: very subtle indeed. Keep up…
Alan 27 Apr 2015 10:29 pm: How can it be proves that “dividing by zero on both sides…. invalidates the equality.”? Isn’t the correct answer to 0/0 = we don’t know?
Lolguy 4 Dec 2014 9:52 pm: The number 2 is wrong. It should read like: sqrt(1) sqrt(1) = sqrt(-1) sqrt(-1); sqrt(1) = sqrt(1); (since sqrt(-1) x sqrt(-1) = sqrt(-1 x-1) = sqrt(1)) 1 = 1
Fabricio 21 Dec 2014 1:48 pm:

The number 2 is wrong. It should read like: […]Lolguy,The second proof is wrong, yes; though not for the reason you stated (which is also wrong reasoning).The error in the proof is the third line, sqrt(1/-1) = sqrt(-1/1) , which does not make sense, formally; even though it looks suggestively meaningful.The implication from the second to the third line would be equivalent to saying that,Carl is the same person as Carl, [ Carl = Carl ]Therefore, [any] son of Carl is the same person as [any] son of Carl. [ son_of(Carl) = son_of(Carl) ]This will only be always true if Carl has only one son; evidently, if he has more than one, any two given sons of Carl need not necessarily be the same person.A analogue situation happens when defining the square root of a number:In context of the set of real numbers, it is possible (and actually done so, in many places) to define the square root of a number x as ’the positive number y, such as y^2=x’ ; (The generalization for n-th roots, n pair, coming easily from that, in an analogue manner.)This solves the issue for square roots (or any other roots) under the real numbers: defined in this way, they determine a function (a relation between sets A and B, such that to each element in A one, and *only* one element in B is associated) and can be used as an operation that can be applied to both sides of an equation and still preserve its truth (in the same way it is valid to state that x = y implies that x^2 = y^2 , or that x = y implies that log (x) = log (y) ).Defined in this way, sqrt(x) constitutes a function, and does, as all functions do, possess the property of being a univocal relation: for each x, there is only one f(x), or in this particular case, only one sqrt(x).When it comes to the set of complex numbers, though, the plot thickens, because for any given non-zero complex number z, there will be n different complex numbers z_i (i = 1, … , n) such that (z_i)^n = z .It is said, usually: ’each complex number z has n complex nth-roots.’ (Thus, 2 square roots, 3 cubic roots, and so on.)Now this way of defining z_i as being an n-th root of z does not have the property of being univocal, and therefore does not constitute a function and cannot be used as an equality-preserving operation applied to both sides of an equation.This is why -1 = -1 does *not* imply that sqrt(-1) = sqrt(-1) ;After all, i^2 = -1 and, therefore, it is a complex square root of -1 (qualifying to be on the left side of the second equation),;At the same time as (-i)^2 = -1 and, thus, is also a complex square root of -1 (and could be on the right side of the second equation).Evidently, -i = i is false, as they are distinct complex numbers.It is worthy noting:The definition of a complex root could be restricted to make it a function.It could be that *the* complex n-th root of z is defined to be the number w with the smallest argument (the angle theta in the complex plane representation of w) such that w^n = z .This, however, is not done anywhere. Rather, the concept is defined by saying that w_i is a complex n-th root of z if w_i^n = z . And that implicates that there is more than one n-th root (for n>1). The complex root thus defined is sometimes said to be a ‘mutivalued/plurivocal function,’ in textbooks.(This is usually carried on to extend the concept of function, and does not mean that the complex root is a function proper. It is a case of ‘abuse of language.’ See https://en.wikipedia.org/wiki/Abuse_of_notation )Thus, when you write sqrt(-1) and look down at it, in the paper, no matter how suggestive it is of being ‘a number,’ it is not.It is but an abuse of language by which you are representing different numbers with one single graphical symbol. And therefore it cannot be used in equations in that same manner that you use ‘x’ , normally.While x represents, in the context of the equation, only one number; sqrt(-1) represents more than one number and therefore, sqrt(-1) = sqrt(-1) is wrong.Abuse of notation can be used effectively to produce correct results, if communications, or reasoning, take place between two parties that are well informed and conscious of the limitations of the notationally abused language. What is gained, many times, is a more compact way of expressing ideas well known to both parties.For instance, it can be economical to write and think 1/0 = infinity, or, lim (1/x) as x->0 = infinity, even though, strictly, both of these ’equation-like’ arrays of symbols have no meaning.If both parties are well trained in the definition and properties of limits, the shorthand notation can be used to perform calculations correctly, saving a great deal of paper and time needed to write formally correct statements regarding the (non-existent) limit of 1/x as x approaches 0.The danger here, is uninformed third-parties reading those and due to lack of training, drawing false conclusions.

Even understanding it all, it is not uncommon, from time to time, for one to come back to those false implications/proofs using sqrt(-1) and scratch one’s head, while going ‘damn… I know this is false, but, why, again?’ Notational intuition is a powerful force within your mathematical brain. (And it shows in the history of mathematics, in episodes where bouts of prolific development in theory come right after some better notation gets introduced.) You might wanna memorize a formalist mantra designed to safeguard you against this particular situation: ‘Sqrt(-1) is not a specific number. It cannot be hurled around inside equations just like x.’ Repeat ad nauseam until all thought is drowned. :p Put this formalist mantra in your personal mantra library along with ‘Thou shalt not divide by zero.’ and also, ‘The square root of a^2 is modulus of a, and *not* just a.’ (which helps you avoid the common and tempting mistake of assuming that a^2 = b^2 implies that a = b ) Cheers, Fabricio
Ignis 5 Nov 2023 3:25 am: X≠Y, but 0=0 so X=Y 🤪

What programmers do

Tue, 04 Apr 2006 12:00:00 +0000

What programmers do.

OReilly Hacks

Wed, 25 Jan 2006 12:00:00 +0000

O’Reilly hacks.

Market emergence - fan bartering

Thu, 05 Jan 2006 12:00:00 +0000

Over my last few years as a consultant, I’ve seen many interesting ways in which markets have emerged where they shouldn’t have, creating havoc in pricing and scarcity. Fixed prices fluctuate, free goods acquire a value, and non-tradeable goods are traded. I’ll share a few of these examples over the next few weeks.

Once, a fan manufacturer asked us, We did an analysis and found that our wholesalers’ margins fluctuate. How could that happen, when we are fixing their buying and selling prices?

The manufacturer sells several popular fans. Their highest selling fan (call it HS), for instance, was sold to wholesalers at Rs 1,089, who would then sell it to retailers at Rs 1,100. No question of margin fluctuation.

I took a trip to Lohar Chawl, the wholesale fan market, to get to the bottom of this. After a few conversations in dingy warehourses, here’s what I discovered. Fans are bartered. Wholesalers keep as little cash and inventory on hand. Often, a retailer would order a fan (say X) not in stock. The wholesaler doesn’t want to lose the deal, and doesn’t have cash, but he would have some inventory of HS, since it’s such a high-selling fan. He goes to another wholesaler, and says,

“Give me some fan X, and I’ll give you some HS fans instead. You’ll be able to sell these HS fans fairly quickly anyway.”

“Why should I? Tell me your customers name and I’ll sell it to him myself, and make the profit.”

“Tell you what. I’ll give you my HS fans for Rs 1,079 instead of Rs 1,089. You’ll get a higher margin when you sell it.”

This is a routine matter in Lohar Chawl. If you don’t have a fan, barter it for another (often HS) at a discounted price. So the wholesaler’s margin would depend on how many fans they bought at a bartered price!

Poaching was another reason for the margin fluctuation. The manufacturer demarcated territories for each wholesaler, saying “You can sell the these 20 retailers, you can sell to those 18, and so on.” Ambitious wholesalers, or those with inventory to dump, would do a side deal with a retailer.

Look, your wholesaler charges Rs 1,100 for this fan. I’ll sell you this lot for Rs 1,095. And let’s keep it quiet."

Yet another reason for margin fluctuation was smuggling. Sometimes, the wholesalers would be able to smuggle fans into Mumbai without paying octroi. And sometimes they wouldn’t.

The biggest lesson for me from this was, It’s bloody tough to restrict a free market. I’ll tell you more about this shortly.

Comments

ritzkini 6 Jan 2006 6:25 am: :) Bloody tough indeed ! lemme guess,these were all gujjus !rite ?? ingenuous, i tell you,these guys..
Arun 6 Jan 2006 8:27 am: Neat! Thanks for those Excel tips. And look forward to more of these!
Madhu 6 Jan 2006 12:10 pm: I have noticed instances where a TN Auto Distributor comes and sells his stuff to a Karnataka retailer! How did you solve this problem? in my case, which was personal advice to a friend, we wrote to the company with some of the fake bills etc and asked for a higher discount for my friend who is a karnataka distributor, things like CST also start to matter in inter-state things. now the problem has come down bcos of VAT
S Anand 6 Jan 2006 4:50 pm: I did this work as part of a proposal. We finally didn’t get the project. But I suspect (and will try and show over the next few posts) that this is a problem that’s probably not worth fighting. The market will eventually win!
Madhu 7 Jan 2006 11:53 am: Ideally a very good supply chain management system will help solve this problem atleast. For eg: If i can order and get it immediately instead of having to bargain. Another issue is how was fan X priced? If its lower than 1089, it will also solve the problem
S Anand 7 Jan 2006 7:15 pm: The problem wasn’t supply chain lead-time, but shortage of cash for inventory among wholesalers. Whenever they were short of stock in one fan, they’d sell some other fan they had as inventory to get the fan they were short of. They can’t order it from the manufacturer, remember: they’re short of cash. They NEED to barter.
joe 7 Jan 2006 11:39 pm: the fan company had no clue why the margins were fluctuating ? scary thought. how could they not know about this. I presume it is top management that did not know this
Madhu 8 Jan 2006 3:53 am: Ok. A SCM which can even take in account demand considerations is ideal. But how can the HS and X be priced the same to the retailers? Isnt that failure of the market? Shouldnt a HS fan be priced different(higher?) than some random fan X?
S Anand 8 Jan 2006 10:52 am: Madhu, you’re right. The fans ARE priced differently. So it won’t be a one-to-one barter. If Fan X is priced at 1000, the wholesaler will give agree to sell 10 HS fans at Rs 1079, give 10 HS fans PLUS 790 Rs, and get 10 Fan X in return.
S Anand 8 Jan 2006 10:54 am: Joe, even the line mgmt didn’t know about this bartering! One of my colleagues discovered it. This guy’s a god of black money market operations, incidentally :-)
shyam 9 Jan 2006 10:07 am: This is something similar to the SJP Road market in Bangalore where u can buy computer parts at " SJP Road price “. the shopkeepers will undercut even the wholesaler price and sell it for " cash "

Think like a genius

Thu, 23 Jun 2005 12:00:00 +0000

Think like a genius.

10 steps for boosting your creativity

Fri, 25 Feb 2005 12:00:00 +0000

10 steps for boosting your creativity

If you’re stuck for an idea, open a dictionary, randomly select a word and then try to formulate ideas incorporating this word. You’d be surprised how well this works. The concept is based on a simple but little known truth: freedom inhibits creativity. There are nothing like restrictions to get you thinking.

Realistic lateral thinking puzzles

Mon, 06 May 2002 12:00:00 +0000

Realistic lateral thinking puzzles.

Lateral thinking puzzles

Sun, 07 Jan 2001 12:00:00 +0000

It’s been long since I solved lateral thinking puzzles. Hartman’s site has over a hundred (with answers).

Boston Consulting Group Interview

Sat, 25 Nov 2000 12:00:00 +0000

First Round

On Saturday (25th November 2000), I dress up in my best suit (only suit, really), and find my way to the Green Park station for an interview with the Boston Consulting Group. Of course, being terribly conservative, I arrived an hour early, so it was time to walk around Green Park and have a look at the Buckingham Palace, while singing “I have confidence…” from Sound of Music. The walk did lift my spirits a bit. There was this tiny poodle that was busy licking a bulldog. The bulldog didn’t seem to mind, though it was large enough to eat up the poodle. Then the poodle’s owners picked it up, and walked away. The poodle was reluctant though. It just hadn’t finished licking the bulldog. After about 5 minutes, the bulldog (and owner), were about half-a-kilometer away, when the poodle was finally let down. Being the determined creature that it was, it ran ALL the way to the bulldog, and proceeded to lick. The bulldog, right through, was wearing a puzzled expression on its face, as if to say, “Are you sure you don’t want me to smack this little white fluff?”

At 10:15AM, I walked in to the BCG reception, and was led to the cafeteria. I was only carrying an umbrella (which I left at the reception), and some sheets of paper. There were to be 2 case interviews, each for 45 minutes. I was told that I’d be interviewed by Danai and Kim Wee. Danai (who’s from Bangkok) came along, and took me to a conference room. The interview begins.

Danai: “Hi Anand. Let me tell you a bit about how this interview is structured. We’ll begin by discussing your resume a bit. Then we’ll move on to a case, and finally, you can ask me any questions that you want. The reason we do a case interview is to test the candidate on 3 things: their enthusiasm for problem solving, their analytical skills, and communication ability. Let me begin by introducing myself. (Introduces himself in detail). Could you tell me a bit about yourself?”

Me: “Uh, sure. I studied at IITM. Nice place. Then I worked at IBM. Nice place too. Then I went to IIMB. Yet another nice place. Now I’m at LBS. Pretty nice. Uh…” At this point, I completely ran out of things to say. I mean, I’d been training for this and all that. But at the point, your mind just goes blank. So I said, “My hobbies include…” – and couldn’t think of a single hobby. My resume lists several, but the first thing that came to my mind was one that was NOT on it: “Acting.”

Danai latches on to this. “Wow, that’s interesting. So what would you like to be? Director? Actor?”

“Oh, acting itself. Writing the script too. One of my dreams is to be a film hero. " I actually said that. It had gotten to the point where I was desperate and willing to blabber anything to recover. “I like it because it involves a lot of communication and I’m good at communication.”

Danai neatly caught on. “Yeah, there’s a lot of communicating that you’ll have to do in consulting as well. Good. Tell me about (some point on my resume).” Then we discussed my resume a bit. Then we got to the case interview. Right through, Danai was taking notes on what I was saying – in fact, he wrote nearly 3-4 pages of what I said, as opposed to me who scribbled in half a sheet.

“I’m going to give you a cement company case, because I’ve worked in the cement industry.” Fine by me. “Our client is a global cement manufacturer, who operates in North America, Europe and Latin America. They buy some of their cement from other companies, and produce the rest. They are evaluating entry into Asia. Could you help them?”

Me: First, I’d like to know more about the company. Why are they buying cement from others?

Danai: They’re not all that good at manufacturing. I mean, they’re pretty good, but nothing extraordinary. Their main strength lies in marketing and logistics. They only have 50% of the capacity of their sales.

Me: OK. Why do they want to expand to Asia?

Danai: Why do you think?

Me: Several possibilities. Maybe they want growth, which they don’t have right now. Maybe there’s a one-off opportunity in Asia right now. Maybe there’s tremendous growth in Asia and they don’t want to miss out on it.

Danai: What could a one-off opportunity be, for example?

Me: Deregulation is a classic. Another is just a first mover advantage. Hmm… that’s all I can think of.

Danai: You’re quite right about all three. Their growth is slow. There is a window of opportunity in terms of regulation, and the company believes there is lot of potential in Asia. Let us take Thailand as a representative market and work on it, because I have worked there, and can give you answers to your questions. How should our client enter the Thailand market?

Me: Well, this is what I’m going to look at: the market in Thailand, the competitors in Thailand, the resources of the company (people, money and machines), and the regulatory environment (repatriation, licenses, etc). What can you tell me about these?

Danai: Let us assume that the company has the requisite resources, though that is a good point. The regulatory environment is also friendly and the clearances are easy. The market is dominated by 3 groups of buyers – government contractors (40% revenue), private contractors (30%) revenue, and a network of retail shops. There are a few large players in the market, the top 3 taking up 70% of the market.

Me: What are the parameters on the basis of which customers base their decision to buy?

Danai: It’s as follows (in decreasing order of preference)

Government contractors: Price, reliability of supply, relationship

Private contractors: Price, reliability of supply, brand name

Retailers: Brand name, reliability of supply, price

Me: OK, looks like price and reliability are pretty important. What is the competition like? Is it stiff? Are there price wars?

Danai: What causes price wars?

Me: Well… is there excess inventory?

Danai: Precisely. There’s a lot of excess inventory, and that has resulted in a price war.

Me: Are these companies inefficient?

Danai: In manufacturing? No. The whole world is pretty much the same in terms of efficiency. They are not that good in marketing and logistics though. But this constitutes only 10% of the costs.

Me: Right. The way it looks now, it seems crazy to enter a market that’s got high inventory and price wars. I mean, even if you cut the logistics cost by 50%, it’s still just a 5% reduction in a market that goes by price. No way. Looks very unattractive. But let’s not dismiss it. How about a joint venture?

Danai: Why would a company do a JV?

Me: We’ve got the marketing power. We’ve got the logistics capability. We can partner. We should just pick a company that’s going almost bankrupt, and tell them to sign up.

Danai: Would that suffice? What would they want from us?

Me: Well… access to international markets, I guess. So we can ship the excess inventory to neighbouring countries using our superior logistics.

Danai: Good. How would you go about such an exercise?

Me: (I explain how to pick a company, how to negotiate the contract, and so on.)

Danai: Fine. Do you have any questions for me?

Me: I want to teach part time. Can I do that? (Yes). Is it true that consultants are only rubber stamps of the CEOs? (No. Otherwise, we would’ve lost our reputation.) What does your day look like? (Go to office, have meetings with clients, have meetings with team, solve problems, travel a lot).

By then, it was time to meet Kim Wee, who was in the next room. The previous night I’d run through their website, and had found out a bit about Kim Wee, which I remembered. That kind of gave me some confidence, and I thought of a nice opening line like, “You look much better than in your photograph” or something like that. But when she started off, I realized I had no chance of getting a word in.

She began with, “Hello Anand. Nice to meet you. This will be the same format as Danai’s interview. I’ll quiz you on you resume, then we’ll do a case. Then you can ask me questions. Can you tell me about your experience at Lehman Brothers?”

This entire speech took 3 seconds or so. At least, that’s what it seemed like. Completely expressionless, and ununderstandably fast. My response was very coherent, though.

“Sorry?” (This was my most frequent phrase through the interview, followed by, “Huh?”)

“Can you tell me about your experience at Lehman Brothers?”

The meaning was obvious. So I said, “I never had a choice. The tyrannical placement rules at IIMB don’t give me any choice at all. So I was tied in chains and forcibly shipped to Tokyo for slave labour. I didn’t eat or sleep. Of course, I like that sort of a thing – even if you slave-drive me, I’ll be happy. But I want to have an influence on the world, and make it a better place to live in, which I can’t do from a bank. So I’ve decided to be the knight in shining armour (OK, consultant), and…”

She cuts me off with a monotonous, but quickfire, “What’ll you do in the future?”

Me: I’ll become a freelance consultant.

Kim: Why?

Me: That way, I can say no to a client if I want to, and still solve problems, which is what I like doing. Besides, there’s a visiting Prof at IIMB who’s doing that, and I’m kind-of using him as a …

Kim: What challenges will you face as a consultant?

Me: Huh?

Kim: What challenges will you face as a consultant?

Me: (a few ‘huh’s later) I hate telling CEOs what they want to hear. If they’ve made up their mind, I’ll tell them to shove it and walk away. In fact, I …

Kim: What is your most memorable accomplishment?

I was lost again. My prepared answer was the IBM India home page. But NOTHING came to my mind. After a few blank seconds, I figured I had to say something. So I said, “I shared reports at IIMB.” She stared, and I figured I had to elaborate. “I wrote great and wonderful reports. The Gods praised them, and ordered me to be fruitful and share. So I did. Then everybody started sharing.” (I was completely out of my senses by this time) “So now, there is a HUGE library of reports at IIMB. It’s going to be extended to all IIMs. Maybe all universities in the world. And it’s ALL my work. I’m terribly proud of it, etc. etc.” (OK, I didn’t say all that, but I came close.)

Kim, for the first time, not interrupting, and speaking relatively slowly, “There was a problem at NTU with this. The professors stole the reports and passed them as their own.”

Brilliant. All I could come up with was, “Thanks for pointing that out. I hadn’t considered that. I’ll let the students at IIMB know of this danger.”

Then we moved on to the case. “Our client is a food processor. One of their products is Cool Wave (or something like that). It’s a non-dessert cream topping, with 40% of the market share. They have excess capacity. Though the industry is growing at 6%, the sales of Cool Wave is flat. You have to find out why and give recommendations. Then you have to move on to other products.”

The interview went on for a gruelling half-hour. I can recall the details, but it’s too painful for that. Most of the time, I kept asking questions to which the answer was, “We don’t have that information right now. Maybe it could be this. Maybe it could be that.” Then we’d agree on something. After 5 minutes, I’d say something, and she’d come back with, “But how can you say that?”

“Because we agreed on this 5 minutes ago.”

“Well, we don’t have that information. Maybe it could be this. Maybe it could be that.”

Wonderful!

Finally, I did manage to piece together that the dominant competitors were pricing 15% lower, and the rest (fragmented) were pricing it 30% lower. The lower-income group was now able to afford the product. So the market was growing at the bottom, and since Cool Wave was a premium brand, they couldn’t capture that market share.

Me: One possibility is to reduce the price of Cool Wave. But that’s a bad idea (I give reasons). Another is to introduce another brand at the low end.

Kim: Anything else?

Me: (Struggle for 2 minutes. Then…) No idea.

Kim: Well, they could just sell the capacity to Wal-Mart or somebody, who could make their own-brand of the topping and sell it at the low-end.

Then I caught on to this idea, and began giving recommendations on how to do it and stuff like that. I was into my conclusion, “So they should ensure that the contract with Walmart does not appear hostile to their other retail customers…”

Kim: OK. Case is over. Do you have any questions for me?

Me: Sorry? The case is over?

Kim: Yes. Any questions?

Me: About the case?

Kim: No. Case is over. Any questions?

Me: (After about 10 seconds) Yeah. What is work like at BCG?

I don’t remember the answers. I don’t think I even heard them. They were too fast for me. Anyway, she ran me out of the building, and, as I picked up my umbrella from the reception, said that she’d let me know by Sunday evening if I got through.

I made my way to LBS, wondering if my chances were even 50-50.

Second Round

Anyway, I got through to the second round, to be interviewed by Marcus and Joon. Marcus asked me, quite casually, “This isn’t a case, really. It’s something I’ve been asking a lot of people and haven’t found a satisfactory answer to. Why is it that hotels charge you when you book a room and don’t turn up, but rental car companies don’t charge you if you book a car and don’t turn up?”

To cut a long story short, I really thought Marcus (who was a VP) was just casually interacting. So I just had a casual conversation with him, exploring some possibilites. I wasn’t getting anywhere, but I didn’t worry. I thought the point was to test how cool I was under uncertainty. Turned out to be a complete mistake. Anyway, after half an hour of pleasant conversation, Joon came over.

Joon said, “There’s an airline company that ships freight. It has passenger planes as well as freight planes, and uses both to ship. They have been losing money recently. Why do you think this is so?”

This proved as straight-forward case, and was over in 15 minutes or so. In fact, Joon volunteered most of the information himself. I was so thrilled that I left my umbrella in the office and walked off in the rain.

A couple of days later, Joon calls up from Kuala Lampur. “Hello Anand, this is Joon from BCG.”

My heart starts thumping. Is it a yes? Is it a no?

“We were very happy with your resume and your qualifications. However, we are very sorry to say that we are unable to take your application forward at this point.”

It’s a long distance phone call, so he had to pause for my response. Which was something like “(croak) Of course.”

“We are extremely sorry, but hope you had a good experience through the interviews.”

“(cough) Of course.” I was brain-dead by the time anyway.

“Would you like some feedback about your performance?”

“(glug) Yes, of course.”

“We felt that you did not have the analytical skills. When Marcus and I discussed, we felt that your interview did not have enough structure.”

By this time, I’d found my voice, so I managed to mutter something like, “Thank you very much, Mr. Ooi, I’m sure the feedback will be very useful. It was a pleasure interviewing with you. Bye.”

So there it is. Lack of structure. I’ve been told that before, of course. Got to work on it…

Comments

Sai 13 Nov 2006 7:46 pm: Anand, i commend you that you remember everthing that happened, especially the first interview. But i thought that you worked at BCG, so how come i see here that you did not get through?
EE 7 Dec 2006 6:58 pm: That was a very interesting story. I had a similar experience with McKinsey in one of their US offices recently - ding in the final round. I don’t have any business education though - Btech EE from IIT-B and now close the end of a PhD in ECE. I would love to talk to you about how to improve the “structure” - because that is one of the reasons why McKinsey did not like me in the end. If you are willing, please reply to this note.
Ap 2 Jan 2007 4:28 pm: Anand, Thanks for recounting your experiences interviewing with BCG. As someone who is interviewing with them for the first time - I would really appreciate any pointers on improving structure - I didn’t make some comparable firms because of this issue.
saurabh 29 Mar 2007 12:31 pm: This was motivating for me. The vagueness of selectors has always caused me a lot of pain. You bring it out quite succinctly and sardonically.
swethaN 25 Nov 2000 12:00 pm: Really interesting one.
Kaviraj Nair 25 Nov 2000 12:00 pm: Anand!! long time man…..i chanced on your website as I was searching for Viriboni varnam in google…(I am learning that in my class now!!)…..it took me to ur Carnatic page and I was thrilled to see your website flourishing with newer branches around!!……..and then browsed the site to read this write-up……..very hilarious……..!! anyways, how have u been? Best Kaviraj NAir
T.C.Srinivasan 14 Aug 2008 4:20 pm: thank you for giving insight of what consultant expects in a interview
Kyrylo 10 Nov 2008 9:26 am: Hi guys,

Occasionally, I ran on this post. First of all, thank you for the experience you shared!

You know, I want to submit my CV to BCG and even before having the interview I imagine the answer “lack of structure”. Thus, if you guys know how to work on this issue I would really appreciate your help.
ta23 5 Mar 2009 9:39 pm: Hi guys! I would like to recommend you to read some Plato’s stuff (philosophy). When you read his works, you will find that his statements (actually by Socrates) are not only brilliant as far as content is concerned, but you will discover that he structures them perfectly, utterly comprehensible and easy to pass to others (even though they are very complex matters).
- here is what I have found on the internet, but this seems for me as an easy-version how to tackle the problem, and I don not think that a 2day work can be efficient. Nevertheless worth mentioning. http://answers.yahoo.com/question/index?qid=20080117190910AAzIXIl Good luck anywhere you go! T>A
Trang 3 Nov 2009 12:42 pm: I enjoyed reading this a lot, very useful. I had pleasant first round interviews and now about to have 2nd round (also final round I believe). Not sure if cases are gonna be harder and how I should be prepared (thats why I googled online for BCG interview tips haha) but your post is very helpful while entertaining. I’m sure you can make a good script writer ;)
kiran 11 Oct 2009 5:08 pm: hi dude .. tx .. i was just abt to apply for it now :) i thought i have to do my ground work ..
Tatiane 3 May 2010 1:45 am: Hey, Anand, thanks a lot for sharing your experience on the web. I’m preparing for my interview and it´s really to have this kind of information before it happens! Thanks a lot!
M. Rafik Sama 22 Dec 2009 1:10 pm: I am also working as Visiting Faculty of Strategic Management. Well tried. but I fail to understand where your concept were " Lack of structure”. Will you please put some light on it. so, it will be beneficial for me in my profession.
Amit 4 Sep 2010 6:29 pm: Hi All, am working with one of the big4 Chartered Accountant Firm in Mumbai as an Analyst in Mergers and Acquisition prior to that i was working in Treasury operations in J P Morgan Chase. can anyone here help me out to make it to BCG……
Sanghamitra 22 May 2010 10:21 am: Thanks Anand for sharing this. It really insightful…..and specially because I am right now working on “no structure” problem. Would be happy to hear of any suggestion if you have for me.
Vaidy 4 Dec 2010 5:46 am: Hi Anand, Good piece and thanks for sharing, I am on my way preparing for the interview and if I read between lines, the interviewer was more on the EFAS and IFAS with his discussion route leading to SFAS, well I hope to do well and will be in touch for some tips
Frank Castle 21 Nov 2011 11:05 am: Thanks for giving such wonderful ideas and suggestions. Plz keep writing on such interesting topics. Thanks for sharing this information.
Partha Srinivasan 9 Jun 2011 6:21 pm: Hi, your blog is very interesting and written in a satirical way.. :)…I looked up your linked in, so it appears you did make it to BCG eventually. Could you please publish that story ? Thanks, Partha.
Andre 18 Apr 2011 5:50 am: I just read your hole story. It is interesting and very well written. How old were you by that time ? Did you ever join a Consulting Company ? What are you doing nowadays ? Sorry to ask. I mean I have nothing to do with it except my own interest. I am a recently graduated engineer. Took 3 exams before they invited me for my first round of interview and this is next week at the BCG Office in Sao Paulo, Brazil. I want it so bad and I am putting so much effort on it that I can sorta guess how you felt getting that negative answer back. Hope you are doing good ! Thank you for sharing it I feel even more prepared right now. If you can answer me my email is listed.
S Anand 10 Jun 2011 1:55 pm: There wasn’t much to that, actually. This interview was at LBS during my exchange. I attended placements again at IIMB and got through :-)
calvin 14 Feb 2012 9:15 am: I will be interviewed as local specialist on thursday at BCG Jakarta, I found your post is very helpful. did you have phone interview though? I will be interviewed with someone from BCG India. I’m quite nervous because I’m a graduate from international relations, though I’m interested in economy and finance in general. I just hope I could pass the interview cases…
Riddhi Mohan 29 Feb 2012 7:31 pm: Very Informative and the way to come up that is even more interesting. Landed to your blog seeking something and found more than what i was looking upon. Thanks for sharing.
Sauarbh 14 May 2014 6:16 pm: Thanks for this,but still could not get,why lack of structure