If you have one bucket of water with 7.5 litres and another bucket with 2.5 litres, how many buckets do you have ?
Teacher: Billy has three fingers on one hand and two fingers on the other. What does Billy have?
Student: A disability!
A student goes shopping for a television,he see's one in a shop window priced at £30..He has no money so he asks his friends to borrow the £30..When he goes into the shop to buy the TV,the shop assistant tells him the TV has been reduced to £25..After much thought the student has an idea...He gives his friends all £1 each,therefore they've only payed £9 each and he puts the £2 in his pocket...3x9=27+2=29 where is the £1
A student goes shopping for a television,he see's one in a shop window priced at £30..He has no money so he asks his friends to borrow the £30..When he goes into the shop to buy the TV,the shop assistant tells him the TV has been reduced to £25..After much thought the student has an idea...He gives his friends all £1 each,therefore they've only payed £9 each and he puts the £2 in his pocket...3x9=27+2=29 where is the £1
I don't know the best way to explain it. The most complicated way I think is to point out you added the two twice and forgot the 3 (and 29-2+3=30). I say you used the 2 twice because 2 is part of the 27 left over after he gave 3 back, meaning you can't add it again. So it should be 25 + 2 + 3 or 27 + 3.
The simplest way I can think of to explain it is in terms of input and output. Input 30. Output 3, 2, and 25. In this way you see 27 is part input (25 of 30) and part output (2), so you can't add them. Additionally if you want to multiply something by 3 it would be 10x3 (all input).
So if this story confuses a person the reason is likely the mixing of input and output on the number 27.
Maths-Geometry, algebraic notation,calculation,problem solving,systematic,8 by 8 board,"what if" statements,values to chess peices,spatial awareness and imagination.
Sounds like chess to me!
No. No use for integrals or goniometrics.
OK two things is perhaps not proof enough. No use for Matrix calculations either. Or DIV ROT GRAD. Or Laplace.. Not related
Chess, mathematics. Yes. All 3 of them are related.
Nice, beardog!
Since chess can be described in purely mathematical terms, it is of course related to mathematics. It's a type of math.
Nice, beardog!
Since chess can be described in purely mathematical terms, it is of course related to mathematics. It's a type of math.
I had read about a graph-theoretic intepretation by W.T. Gowers.
both are the domain of dweebs!
related!
So at first all three friends gave $10. The student had $30; $25 of that went to the store. He has $5 left. The student decides that he can pay each of his friends $1 back so he gives $1 each. There are $2 left, which he keeps.
$27 could represent the debt the student has to his friends -- he was at first $30 in debt, and now he's $27 in debt because he gave three. There is no reason why we should use this to solve the problem.
So the problem with using 9x3 + 2 is that it simply doesn't represent the situation -- the flow of the $30, and is irrelevant to the problem. The fact that it happens to equal a number close to $30 is merely incidental.
As for the similarities between chess and math: they are certainly there, but they are obviously not the same thing. I think chess is a lot like art too, and yet I hate painting or drawing. You'll probably find lots of people who like chess and math, but you'll probably find people who only like one of those things as well.
Yes but he got the TV
All of that is accounted for in the first paragraph. That is the way to go about solving the problem; no need to use this "27" idea.
I guess another way to look at it would be this (not any more correct than my first paragraph of the preceding post, but this might be more illustrative of why the 9x3 + 2 didn't make sense): As we know, the student is in $27 of debt because he received $30 and only 3 of it went back to his friends, 30 - 3. Of this borrowed, unreturned money, 25 of it was spent at the store, while 2 of it was kept. As Wafflemaster said, this could be represented by 25 + 2 (the debt when separated), or you could just say 27, and then +3 to that, the 27 being debt, the 3 being non-debt.
So the $2 that is kept shouldn't be added on to $27, because it is part of this $27. These two dollars were not given back, so it makes up a portion of this $27 of debt.
A student goes shopping for a television,he see's one in a shop window priced at £30..He has no money so he asks his friends to borrow the £30..When he goes into the shop to buy the TV,the shop assistant tells him the TV has been reduced to £25..After much thought the student has an idea...He gives his friends all £1 each,therefore they've only payed £9 each and he puts the £2 in his pocket...3x9=27+2=29 where is the £1
if he gives them £1 each back, he has £27.
He keeps the £2 after paying £25 for the digital picture.
27=27
They gave him £30, he gives out £30 in £25 to the shop, £3 to the friends, £2 for himself.
30=30
The equation isn't 3x9+2=29
it's 3x9=25+2
or 3x10=25+2+3
And all this time I just thought he was pocketing the money...
Ye....A swimming pool is 25m long and yeh deep but you don't think about that while your swimming.
Not true, you count distance traveled in meters (or here, 25 yard pools so in yards).
Tim your missing my point..Mathematics is in everything...Everything!
It is only reference...Take the "fern" (Fractals).But when you look at it, it is pleasing to the eye,you don't start making calculations.
A musician whom plays an instrument..(Mhz).but he doesn't make calculations,he listens and responds.
Let me try it this way:
One of the earliest applications computers were taught was how to play chess. Chess can be expressed and understood entirely by mathematics. Can mathematics also be artistic? Yes, one only needs to think of some of collections of fractals and mandelbrot sets to see the beauty of mathematics.
Chess is a form of mathematics.
Yes they are related.
1.You see there are 64 squares (not overlapping)/unique thus 8 rows(Ranks) and 8 columns (files). 8x8=64 isn't it !
2.In the King and pawn endgames, the basic ideas rule of square is nothing but simple maths/vector physics, as the shortest path is generally along the diagonal/hypotenuse.
3.Openings can be thought in terms of probability if you are good at mathematics.
4.King's value is infinite, he's everything in Chess !
And whatever you folks want to add here, because I love life sciences more than maths but I remember how most GMs put a comment like Geometry of position etc,. So there may be link between chess and Math and by the way why I want to give complex examples?, simple a1,a2,a3..h1,h2,h8.. is a counting isn;t it so definitely there's gotta be relation.
And not to forget those stats that chess.com gives, they are all pure maths.