Interesting links to various resources on the internet

Over the course of the past couple of days, I have come across a number of exceptional resources relating to mathematics, computer science and popular science. Here are a couple of my favorites:

• Crazy Questions at a Google Job Interview.
• A free book on Abstract Algebra (is VERY useful for solving difficult logic questions in mathematics, provided you can understand it)
• The Best Linux Distribution around - Ubuntu I highly recommend this GNU/Linux OS. It is extremely stable, full-featured, very powerful and exceptionally easy to install. It is also free and has a large community to solve any and all problems relating to it. Down with Microsoft! Long live the Penguins!!!
• I also recommend the Firefox plugins - AdBlock Plus and Stumbleupon.

That's all folks... for now. Please remember to use proper grammar and punctuation when posting on the blog.

N-Puzzle

This is a beautiful puzzle called the N-Puzzle- it is short , simple but in no way sweet. We took it to Lucknow for the IYMC competition for a project display competition.

Ok, so all of us may have seen a sort of game that looks like the image below and played with it when we were kids :-

But here's what a curious person named Noyes Chapman did. He interchanged the position of 14 and 15. Now the basic puzzle looked as follows:-

Now it was given to be solved , that is, the aim was to get the above arrangement from a random arrangement.
And surprisingly, even though it looks easy at first, it was found to be insolvable.

This puzzle is also known by Fifteen Puzzle, Gem Puzzle, Boss Puzzle, Game of Fifteen or Mystic Square.

To prove- Fifteen Square is Unsolvable

Proof:-(Courtesy:Wikipedia. en.wikipedia.org)
The proof involves noting that there are two distinct sets of positions which can be assembled from the pieces with different parity, and there is no way of moving between them using the allowed moves, as they preserve parity. The parity in this context (the invariant) is the parity (odd or even) of the number of pairs of pieces in reverse order plus the row number of the empty square. For the order of the 15 pieces consider line 2 after line 1, etc., like words on a page. Thus an even permutation of the order of the 15 pieces can only be obtained if the empty square is not moved or moved two rows, and an odd permutation of the order of the 15 pieces can only be obtained if the empty square is moved one or three rows.

This small tweaking with the conventional stuff is a brilliant example of how small things can have complex consequences.

Vansh

check out the new version of the mathematica...trial version..

look at the question......dont stare at them....it blocks ur thoughts......

If cubes and spheres could do pots and pans, there would be no tinkerers.

Ok, all your attention are belong to this amazing kind of cube.
Check out why 1=2 is not so interestin...


The impossible cube or irrational cube is an impossible object that draws upon the ambiguity present in a Necker cube illustration. An impossible cube is usually rendered as a Necker cube in which the edges are apparently solid beams. This apparent solidity gives the impossible cube greater visual ambiguity than the Necker cube, which is less likely to be perceived as an impossible object. The illusion plays on the human eye's interpretation of two-dimensional pictures as three-dimensional objects.


Viewed from a certain angle, this cube appears to defy the laws of geometry.

But actually it is not a cube. Viewed from another angle, however, the non-impossibility of the shape is apparent—its cubic nature itself is an illusion.

cool!

Murphy's Laws

Ok, now these are some of the most interesting quotes i have ever read.... or maybe anyone has ever read.

these are my 15 favourite Murphy's Laws on Tech and Logic. there are laws on all topics.

But here are 15 of em which are relevant for this blog.

check em out:

1. Logic is a systematic method of coming to the wrong conclusion with confidence.

2.Technology is dominated by those who manage what they do not understand.

3.If builders built buildings the way programmers wrote programs, then the first woodpecker that came along would destroy civilization.

4.Tell a man there are 300 billion stars in the universe and he'll believe you. Tell him a bench has wet paint on it and he'll have to touch to be sure. great discoveries are made by mistake.

5.An expert is one who knows more and more about less and less until he knows absolutely everything about nothing.

6. The primary function of the design engineer is to make things difficult for the fabricator and impossible for the serviceman.

7.Any circuit design must contain at least one part which is obsolete, two parts which are unobtainable and three parts which are still under development.

8.If mathematically you end up with the incorrect answer, try multiplying by the page number.

9.Computers are unreliable, but humans are even more unreliable. Any system which depends on human reliability is unreliable.

10.If you can't understand it, it is intuitively obvious.

11.Work smarder and not harder and be careful of yor speling.

12. If an experiment works, something has gone wrong.

13.When all else fails, read the instructions.

14. A man with one watch is certain about time. A man with two watches isn't.

15.if it works in theory, it won't work in practice.
if it works in practice it won't work in theory.

The Final round of the intersection mathematics quiz for class X will be held on Wednesday, the 16^th of May, in the AVH at 9:30. The qualifying teams are requested to report there at 9:20 sharp i.e. as soon as the break ends. Carry with you only a pen and nothing else.

The list of the teams that have qualified has already been put up on the notice boards in the CB block.