Umm. The unknown to solve for is the price of the ball. It clearly is an algebraic problem, even if you don't realise that's what you're doing in your head (just to clarify - that is what you're doing).
Paul Wilmott: most quants are stupid
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Umm. The unknown to solve for is the price of the ball. It clearly is an algebraic problem, even if you don't realise that's what you're doing in your head (just to clarify - that is what you're doing).
Daniel Duffy
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How would you explain this simple logic to someone who does not understand it?
In maths theses, as soon as you write "it is obvious" then the alarm bells start ringing.
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I'm arguing that one does not need to have formal knowledge of algebra to solve it.
The question states that the bat costs £1 more than the ball, which infers that the items cost exactly the same if one removes £1.
Thus the question can be read as "Please remove £1 and divide by two."
My claim is that the question so self-explanatory that there is no need to write it out as an equation; anyone with a basic understanding of arithmetic can understand it.
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I think it may be the decimals that are confusing people.
Give any normal person 110 cents. Tell them that one item costs 100 cents more than the other. What's the intuitive thing to do? Make a separate pile of 100 cents. Since one item costs exactly 100 cents more, one can infer that the remaining pile must be divided into two equal piles. Then one combines one of the piles with the 100 cents.
I would argue that they could do. it. Thus I will argue that the original question simply requires a little mental sorting
Give any normal person 110 cents. Tell them that one item costs 100 cents more than the other. What's the intuitive thing to do? Make a separate pile of 100 cents. Since one item costs exactly 100 cents more, one can infer that the remaining pile must be divided into two equal piles. Then one combines one of the piles with the 100 cents.
I would argue that they could do. it. Thus I will argue that the original question simply requires a little mental sorting
Your method isn't one that comes naturally to me, but clearly still works. But the point isn't the method you use to get the answer. The point is to avoid the urge of following your intuitive self's first answer of 10p, which most people can't do.
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Yes, I agree completely. I am a visual thinker and intuitively see everything in shapes and pictures.
It's fascinating that many would intuitively divide by two if presented with only the total, which is faulty, of course, but forget to divide by two when presented with additional information. I guess that was my real point.
Daniel Duffy
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On the other hand if we consider this to be 2 equations in 2 unknowns we can find conditions under which the problem has a solution (i.e. determinant not zero). Then you can dispense with intuition, which is not maths.
So, visually:
x + y = 110
x - y = 100
==> 2y = 110 - 100 = 10 => y = 10/2 = 5.
In mathematics the art of proposing a question must be held of higher value than solving it.
Georg Cantor
So, visually:
x + y = 110
x - y = 100
==> 2y = 110 - 100 = 10 => y = 10/2 = 5.
In mathematics the art of proposing a question must be held of higher value than solving it.
Georg Cantor
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Yes, I agree. I sometimes like to argue for the sake of it, especially on a slow Sunday.
Just to clarify my point: If something cost x amount more than the other, this infers that they cost the same except for x. I argued that this is a function of language and that anyone of normal intelligence would make this inference.
After having tested my hypothesis on a small sample, I have concluded that I was (most likely) wrong. My conclusion is that I am too intelligent to realize the stupidity of others!
Cheers!
Just to clarify my point: If something cost x amount more than the other, this infers that they cost the same except for x. I argued that this is a function of language and that anyone of normal intelligence would make this inference.
After having tested my hypothesis on a small sample, I have concluded that I was (most likely) wrong. My conclusion is that I am too intelligent to realize the stupidity of others!
Cheers!
Yike Lu
Finder of biased coins.
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Actually, I regard the way you presented your solution as an abuse of (linguistic) notation. Everybody seems to have their own natural syntactic habits of form and idiom which they can readily understand.
However these habits often come to woe when discussing math/logic etc with others. I've often come up with a short three sentence explanation of a proof that made complete sense to me, yet completely bewildered others. Not to mention certain passages of Shakespeare make me feel like my brain's parser is broken - like one of those int **&* brainteasers.
This is why we have mathematical notation - I bet if you'd written down the equation, we'd all take one look at what you said and agreed immediately.
Daniel Duffy
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Too clever by half.
So, you cannot explain to someone with below 'normal intelligence'?The problem with language is its ambiguity; using mathematical notation removes this ambiguity.
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