Counting arguments fail, think better!

Here is a puzzle (the answer is below, do not scroll unless you want to see it!):

8809=6            5555=0
7111=0            8193=3
2172=0            8096=5
6666=4            1012=1
1111=0            7777=0   
3213=0            9999=4
7662=2            7756=1
9313=1            6855=3
0000=4            9881=5
2222=0            5531=0
3333=0            2581=?

This one was posted in Lifehacker, the author took it from a flying Facebook post.
The clue provided was that the kids could get the answer faster than the educated thinkers who tend to think in more complex ways.  I can  imagine if your brain is going round the world to solve the problem.
I would urge you to try and guess the answer, which is much fun! Please still do not scroll.
I will even put a youtube video of Simon's cat just to avoid the answer to be seen.





 Please scroll down for the answer.



:)







:)

The answer is
2581=2.

The answer is arrived once you realize that there are two "o" in 8. Go back and check the other answers in the list counting the "o"s in the numbers on the left hand side of the puzzle.

However, this counting argument fails miserably when the numbers are written in another script.
Here, the same example is being provided in coded form of Devanagari numbers. Suppose the left hand side is the code, and right hand is the answer to the code):
८८०९ =6            5555=0
७१११ =0            8193=3
२१७२ =0            ८०९६ =5
६६६६ =4            १०१२ =1
११११ =0            ७७७७ =0   
३२१३ =0            ९९९९ =4
७६६२ =2            ७७५६ =1
९३१३ =1            ६८५५ =3
०००० =4            ९८८१ =5
२२२२ =0            ५५३१ =0
३३३३ =0            २५८१ =?
In this case, You can not count the "o" on the left hand side to arrive at the (same) answer!

 >

--> ---
Symbols: compute the values of the symbols.
Well,  think of the numbers as "variable" So that
०  ०  ०  ०  = 4 means: "०"+"० "+"० "+"० " = ४
 ie 4 of "० " = 4
=> "० " = 1
Similarly,
 ६६६६  = 4
 => "६ " = 1.
9999=4
=> "९ " = 1
and, २२२२ =0 gave: "२ " = 0
 ११११ =0 => "१ " = 0
 ३३३३  = 0 => "३ " = 0
५५५५  = 0 => "५ " = 0
७७७७  = 0 => "७ " = 0
Now do a test case: २१७२  = 0
LHS= "२ "+"१ "+"७ "+"२ " = 0+0+0+0 = 0 = RHS
proved!
Now, to solve, ८८०९  = 6
Suppose, "८ "=y
Substitute values
 y+y+1+1 = 6
 2y+2 = 6,
 => 2y = 4
 =>y=2
Therefore, y="८ "=2

 We tested it for all the examples.
Therefore, we can say:
2581 = "२ "+"५ "+"८ "+"१ " after substitution:
= 0+0+2+0 =2

The answer is 2. The method is more general


The addition is still the counting argument isn't it?
:P

(Thanks to my wife for bringing this solution to my attention.)

Bookworm @ Arxiv visualizing trends #physics

Arxiv.org is a great place to put your papers, which is in waiting for the journal line.
This is also useful to get the time stamp on your work too. Moreover, by putting the pre-print in arxiv, you will be doing a favor to many readers who wants to read your paper off the campus/institution.

They have a tool called bookworm which can search for particular words/terms that you might be interested. It is very handy to visualize how the terms are being used in the published papers.
For example, I searched for the use of "entropy", and mutual information in physics, to get the following graph.

You can use bookworm to visualize interesting trend in the use of terms for the papers submitted to arxiv. Source

See how the use of graphene has "exploded", while qubit is kind of saturated, while superluminal neutrinos spiked recently

As you can see, the  graph is very useful to see the trends of certain terms being used. Please feel free to comment whether it helps to visualize anything about the scientific field.

 

Matlab's Plot Gallery with codes

Matlab is one of the popular software for technical computing.

Everyone has his/her own stories of learning curve with programming. Nevertheless, references and galleries are always helpful when you are at it. 

I would like to suggest you to browse the MATLAB Plot Gallery[Link]. It is a bunch of File Exchange entries from which one can view and download the MATLAB codes.

Happy Coding!

What does pi taste like to the ear?

The number is pi (π). Approximated mostly as 3.14, the march of 14th is celebrated many as pi day. There are arguments whether 22/7 i.e. 22nd of July shall be the real pi day. Moreover, people are also saying that it is merely a half tau day (let me google that for you!)

Anyways, you probably know how pi tastes like. Well, it tastes like a pi. But have you heard how pi sounds like?

Here are couple of videos trying to play the sound of pi (or half tau, if you wish).


You can also go to http://pi.highsign.de/ to compose the pi music.
One more thing: pi-music can not be copyrighted!
>

Grackles fly, merge and cluster in North TX

The Grackle(s) look like crows with extra feathers, little longer.
With the arrival of the Spring, these guys migrate through North Texas. They travel in huge numbers as a group, and can be source of nuisance to some [Link].

As a physicist, it would be interesting to learn about their flocking behavior.
There are statistical physics papers about such behaviors... and Physics Today had a cover story about it 2/3 years(?) ago... Please point the article if you could.

In this post, I present you the flocking swarm of Grackles as they settle down for the night. Please feel free to share.