Second-guessing Puzzles

Good Puzzles are forever. Here are some on a single theme – knowledge of others’ knowledge. The first one is at least 45 years old, read it in बहुरंगी कर्मणूक (Bahurangi Karmnuk). The second one is given in “Elements of Discrete Mathematics” by C. L. Liu, McGraw Hill (1987). The Third one is adapted from “Impossible – surprising solutions to counterintuitive conundrums” by Julian Havil, Princeton University Press (2008).

1. The king summoned the three best mathematians in the kingdom to the palace. The king told them that he had placed either a red or white hat on each one’s head; they may look at, but not talk to, one another (they cannot see their own hats). Each one must raise his hand if he sees at least one red hat on the others, and to lower his hand once he deduces the color of his own hat. First one to deduce the color of his own hat will be rewarded.
Now all three have been given red hats, and each one raises his hand after seeing the others. But none lower their hands for several minutes. Then the smartest one of them lowers his hand, and announces that he has a red hat. How did he deduce this?

2. The king summoned the best mathematicians in the kingdom to the palace. The king told them that he had placed white hats on some and red hats on the others; they may look at, but not talk to, one another (they cannot see their own hats).  The king would leave the room and return every ten minutes. Every time he returns, he wants the mathematicians who have deduced that they are wearing white hats to come up and inform him.
If there are n white hats and m red hats, predict what is going to happen.

3. The king summoned the two best mathematicians in the kingdom to the palace. The king whispered a natural number in each mathematician’s ear. He told them that he had given them two consecutive small natural numbers. They were not to communicate with each other. The king would leave the room and return every ten minutes. Every time he returns, he wants the mathematicians who have deduced the other’s number to come up and inform him.
If the two numbers are n and n+1, predict what is going to happen.

Mere Paas Ma Hai

Amitabh: Mere paas bangla hai, gaadi hai, paisa hai, tere paas kya hai?

Shashii: Mere paas Ma hai.  (Deewar, 1975)

This is surely the most famous hindi movie dialogue to date. I have been collecting variations on this over the years, and now it is time to share. If you know of any more variations, please post them here!

A: Mere paas bangla hai, gaadi hai, paisa hai. Tere paas kya hai?
S: (evil laugh) Tumhari ma hamare kabje mein hain.

A: Mere paas shahi korma hai, Malai kofta hai — tere paas kya hai?
S: Mere paas ma ki dal hain.

A: Mere paas  Solaris 12 hai, Oracle hai, 10 TB ka disk array hai, kya hai tumhare paas?

S: Mere paas root password hai.   (Pravin)

A: (on chat) mere paas web cam hai, skype hai, high speed internet hai, tumhare paas kya hai?
S:  meri girlfriend milney aai hai, ttyl.

Photon: Merey paas energy hai, rang hai, polarization hai, …
Neutron: mere paas maas hai.

A: (in Diwali season) Mere paas rocket hai, bomb hai, chakri hai, anaar hai – tumhare paas kya hai?
S: Mere paas machis hai.

A: Mere paas bangla hai, gaadi hai, barabanki mein agricultural zameen hai,tumhare paas kya hai?

S: Mere paas court ki decree hai.


Mean customer to waiter: Mere paas naam hai, izzat hai, paisa hai – tumhare paas kya hai?
Waiter: Maaf kariye sarkar, mere paas bahut kaam hai.

A: merey paas bangla hai, gaadi, paisa hai, tere paas kya hai?
S: merey paas bhi bangla, gaadi, paisa hai.
A: (long pause) phir ma kahan hai?

S: Merey paas ma hai.

A: Merey paas Paa hai.

Pseudo-Profound Sayings

People appear to be fond of repeating pithy sayings.  This surely started as soon as language itself was invented; certainly people were writing down such things at least thousands of years ago — Marcus Aurelius, Confucius, Ankhsheshonq — and there seems to be a certain pattern common to all of them.

I think the common pattern is that most of these sayings start looking like either tautologies (i.e. stating the obvious) or inane, or wrong, when considered somewhat deeply. Here are some examples:

“The wealth of a wise man is his speech” – Ankhsheshonq (~400 BC). Well, duh. What else can a wise man claim to value? If he says he values gold, or cattle, would he be called a wise man?

“Everything has its beauty but not everyone sees it” – Confucius (~500 BC). Duh again. Sez who – the beholder?

“It does not matter how slow you go as long as you do not stop” – Confucius. That is, if p > 0, then p > 0, where p = progress. On the other hand, this might be very profound observation when you are stuck in Bangalore traffic.

“When anger rises, think of the consequences.” – Confucius. Good advice. But then, the second word could be replaced with several others and still sound very profound – try lust, inflation, CO2, weight, tide, but perhaps not dough. Actually, dough too, if there is too much dough in the pan.

A weapon which you don’t have in your hand won’t kill a snake.” – African Saying. Absolutely accurate — until the invention of remote controlled weapons.

“To the wise, life is a problem; to the fool, a solution” – Marcus Aurelius. And, to the average guy, life is a text book.

“Execute every act of thy life as though it were thy last.” – Marcus Aurelius. Then you must put all your money in insuring yourself, and nothing in long- or short-term investments of any kind. I prefer the more accurate “Act as if you were going to die immediately or live hundred years or anything in-between”.

I close with an example where a metaphor was chosen by a person who did not think through the implications:

“Faith is like electricity – you cannot see it, but you can see the light.”

The complete saying should have been:

“Faith is like electricity – you cannot see it, but:

  1. you can see the light
  2. if you get too close it will kill you
  3. some institution makes a lot of money selling it to you.”