The Maths and Science Thread - Collection of Problems and Facts

[Varun]

How is the name e=mc^2 for a science club?

 

[Chewie]

Too obvious tbh

 

[Varun]

Oh crap. I knew it beforehand.

 

[Aswin8]

nice thread...very helpful,so can i clear my doubts here

 

[Varun]

Yes, sure.

 

[AngryPixel]

Here another nice math fact:

Take any 3 digit number (abc).
Now make it a 6 digit number by repeating the 3 digit number.
(abcabc)
Divide the number by 7
Divide the resultant by 11
Divide the resultant by 13
You'll get abc no matter which 3 digit number you start with.

 

[AkshayC]

Here another nice math fact:

Take any 3 digit number (abc).
Now make it a 6 digit number by repeating the 3 digit number.
(abcabc)
Divide the number by 7
Divide the resultant by 11
Divide the resultant by 13
You'll get abc no matter which 3 digit number you start with.

True

 

[6ry4nj]

Here another nice math fact:

Take any 3 digit number (abc).
Now make it a 6 digit number by repeating the 3 digit number.
(abcabc)
Divide the number by 7
Divide the resultant by 11
Divide the resultant by 13
You'll get abc no matter which 3 digit number you start with.

Ha ha very clever. Multiply a number by 1001, then divide by 1001, and you get the number you started with. Who'da thunk it?!

 

[AngryPixel]

You had to spoil it
Its same as multiplying 2 digit number by 101 and dividing it by 101.

 

[Varun]

Well that was obvious. You just have to multiply 13, 11 and 7 and poof! the result is 1001. Any number abc multiplied by 1001 is abcabc.

I like how people get astonished over these.

 

[AngryPixel]

I need some help in a permutation combination question.
"There are 3 copies of 4 different books. In how many ways can they be arranged on a shelf?"

I have the answer but i don't know how to get there
Answer is : 12!/(3!)^4

 

[Chewie]

12 books that can be arranged in 12 different ways, hence the 12!

However you have to divide by the number of repetitions, and there are four repetitions of 3 books, hence the 3! and you have to divide the 12! by that four times.

 

[AngryPixel]

lol, it was such a simple question. Thanks for reminding this.

 

[Varun]

A question that is intriguing me so much these days - What is the nature of numbers? Or in a mathematical sense, what are numbers really? Are they just an invention to make our work easier, or they have an absolute meaning? If they have an absolute or real meaning, how then do we explain complex numbers? They are numbers as well, but they have a weird, mysterious feeling lying about them. If numbers are absolute, then implying it for complex numbers, does it mean that there is something beyond the absolute numbers that we count/measure that we don't understand?

EDIT : Another update is up in my blog, readers are welcomed if they are interested.