Solution to "Newton's Math Problem" by Shouryya Ray

OR,
Analytical solution of two fundamental unsolved problems of particle dynamics

When I heard that "Newton's math puzzle was solved", I searched for the problem. All I could find was the news with variation of the title: Newton math puzzle, a 350 year old problem, solved by an Indian boy who lives in Germany. Everyone is simply running after the boy and his origin. No description of his work. Yahoo, Google, Bing, all of them capturing the same news item! Of course they show what the interest has been.

The main contribution, which mattered to me, was buried in the pages.

Here is the winner abstract (the webpage was translated using Google translator in Chrome):

• Category: Mathematics / computer science 
• Supervisor: Prof. Dr.-Ing. Jochen Fröhlich, Dr.-Ing. Tobias Kempe 
• Competition Energy: Youth Research

Awards received:

• Second Place in the national competition
• Regional winner
• Regional winner for the best interdisciplinary project

Two problems in classical mechanics have withstood several centuries of mathematical endeavor. The first problem is to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and Newtonian flow resistance. The underlying law was discovered by Newton (17th century). The second problem is the objective description of a particle-wall collision under Hertzian collision force and linear damping. The collision energy was derived in 1858 by Hertz, a linear damping force has been known since Stokes (1850).
This paper has so far only the analytical solution of this approximate or numerical targets for the problems solved. First, the two problems are solved fully analytically generalized context, they are then compared with numerical solutions and, finally, on the basis of the analytical solutions derived statements about the physical behavior.

Original page here:

Youth Research 2012 DD Ostsachsen
And the picture of Ray holding the equation:
https://www.jugend-forscht.de/images/1MAT_67_download.jpg
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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!

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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.)

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!
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