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Topic: Hard: 24 (Read 4375 times) |
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ootte
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24 = 7 * (3 + 3/7)
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Oliver
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i have this answer am not sure if its valid.... but
(sqrt(7*7)*3)+3
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Gamer555
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Re: Hard: 24
« Reply #2 on: Jul 31st, 2002, 6:19pm » |
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I don't think that's too legal....
(Powers and parentheses, and the 4 operations)
For more fun, make 24 with
3 3 3
3 3 3 3
3 7 7 7 (Duh!)
3 3 7 7 7 (The one I got is a bit sneaky)
3 3 5 5 5
Also, with 3 3 7, get 24 1/3
With 3 3 3 7 7, get 24 1/2
(3^3)-3
(3*3*3)-3
3+7+7+7
(73-(7/7))/3
((3^5)-3)/(5+5)
(73/3)=24 1/3
(7*7)/(3-(3/3))=24 1/2
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ya its not:>
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srn437
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the dark lord rises again....
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Re: Hard: 24
« Reply #4 on: Aug 28th, 2007, 12:28pm » |
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3/7 involves decimal points which are forbidden. Exponents and sqrts aren't useable either. How about (3-3)/(7-7) or vice-verca. 0/0 is anything so it could be 24.
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pex
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Re: Hard: 24
« Reply #5 on: Aug 28th, 2007, 12:36pm » |
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on Aug 28th, 2007, 12:28pm, srn347 wrote:| 3/7 involves decimal points which are forbidden. Exponents and sqrts aren't useable either. How about (3-3)/(7-7) or vice-verca. 0/0 is anything so it could be 24. |
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Where is the decimal point in "3/7"? Okay, we could write it as 0.428571 428571 428571..., but there is not much point to it here. And 0/0 is not equal to anything, but you know now. 
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| « Last Edit: Aug 28th, 2007, 12:36pm by pex » |
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towr
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Re: Hard: 24
« Reply #6 on: Aug 28th, 2007, 12:37pm » |
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on Aug 28th, 2007, 12:28pm, srn347 wrote:| 3/7 involves decimal points which are forbidden. |
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How does that involve a decimal points? it's a fraction.
Ootte's solution from 5 friggen years ago is perfectly fine. Just multiplication, addition and division, which are all allowed.
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srn437
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Re: Hard: 24
« Reply #7 on: Aug 28th, 2007, 12:41pm » |
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3/7= 0.4285714285714285714285714285714285714285714285714285714285714285714285 714285714285714285714285714286...
And 0/0 equals anything. And don't evade the word filter system with that word.
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| « Last Edit: Aug 28th, 2007, 12:42pm by srn437 » |
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pex
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Re: Hard: 24
« Reply #8 on: Aug 28th, 2007, 12:44pm » |
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on Aug 28th, 2007, 12:41pm, srn347 wrote:| 3/7= 0.4285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714285714286... |
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As I said, two posts above yours.
on Aug 28th, 2007, 12:41pm, srn347 wrote:
No, it doesn't. Division by zero is not allowed, so (whatever)/0 is undefined: there is no number which it is equal to.
on Aug 28th, 2007, 12:41pm, srn347 wrote:| And don't evade the word filter system with that word. |
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srn437
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Re: Hard: 24
« Reply #9 on: Aug 28th, 2007, 12:49pm » |
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The only reason people forbid it is because they can't calculate a random number or multi-answer equation on a calculator.
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pex
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Re: Hard: 24
« Reply #10 on: Aug 28th, 2007, 12:56pm » |
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on Aug 28th, 2007, 12:49pm, srn347 wrote:| The only reason people forbid it is because they can't calculate a random number or multi-answer equation on a calculator. |
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No: it was forbidden long before calculators were invented.
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srn437
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Re: Hard: 24
« Reply #11 on: Aug 28th, 2007, 12:59pm » |
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Well it shouldn't be forbidden. Just like square roots of negative numbers were once forbidden, which is why they invented complex numbers.
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pex
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Re: Hard: 24
« Reply #12 on: Aug 28th, 2007, 1:02pm » |
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on Aug 28th, 2007, 12:59pm, srn347 wrote:| Well it shouldn't be forbidden. Just like square roots of negative numbers were once forbidden, which is why they invented complex numbers. |
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Correct.
Thus, within the complex numbers, we can say "sqrt(-1) = i"; but within the real numbers, we have to say "sqrt(-1) has no value". Similarly, working within the real or complex numbers, x/0 has no value, whatever x is. If you want to divide by zero, you have to come up with a number system in which division by zero works.
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towr
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Re: Hard: 24
« Reply #13 on: Aug 28th, 2007, 1:04pm » |
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on Aug 28th, 2007, 12:59pm, srn347 wrote:| Well it shouldn't be forbidden. Just like square roots of negative numbers were once forbidden, which is why they invented complex numbers. |
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Well then, invent a number system in which 0/0 makes sense.
There is a good reason why there isn't one.
(And squareroots of negative numbers are still 'forbidden' in arithmetic on real numbers; actually, they're not so much forbidden as that they simply can't be applied there.)
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srn437
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Re: Hard: 24
« Reply #14 on: Aug 28th, 2007, 1:07pm » |
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In the future they'll have a way to define it. I'm already in that process and I'm 13.
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towr
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Re: Hard: 24
« Reply #15 on: Aug 28th, 2007, 1:29pm » |
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on Aug 28th, 2007, 1:07pm, srn347 wrote:| In the future they'll have a way to define it. I'm already in that process and I'm 13. |
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Well, in all fairness, someone already has a number system that gives 1/0 and 0/0 a value. One version is used in computers, try the following in your browsers location bar and it'll give it's values for both.
javascript:alert(0/0)
javascript:alert(1/0)
0/0=NaN, and for any number x, x*NaN =NaN
1/0= +Infinity, and 0*Infinity=NaN, and for any other number x, x*Infinity=Infinity
NaN stands for "not a number"
And there was some noise a little while ago from someone coming up with a slightly different system, which has absolutely no advantage as far as anyone could tell. Even made the news as a great breakthrough, because the media like to pretend they have a clue. (But if they had, they wouldn't have wasted two second on it, probably)
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| « Last Edit: Aug 28th, 2007, 1:30pm by towr » |
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pex
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Re: Hard: 24
« Reply #16 on: Aug 28th, 2007, 1:42pm » |
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That has its own complications, though: NaN is not equal to NaN, for example. (Try javascript:alert(NaN==NaN), if you like.)
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SMQ
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Re: Hard: 24
« Reply #17 on: Aug 28th, 2007, 1:52pm » |
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on Aug 28th, 2007, 1:29pm, towr wrote:| And there was some noise a little while ago from someone coming up with a slightly different system, which has absolutely no advantage as far as anyone could tell. |
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Ahh, yes, Nullity. Just like NaN except  = ... which, as Icarus points out in the linked thread, actually ends up leading to more special cases rather than fewer.
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srn437
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Re: Hard: 24
« Reply #18 on: Aug 28th, 2007, 4:24pm » |
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Not a number?! That doesn't define it. At least it uses infinity.
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towr
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Re: Hard: 24
« Reply #19 on: Aug 29th, 2007, 12:40am » |
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on Aug 28th, 2007, 4:24pm, srn347 wrote:| Not a number?! That doesn't define it. |
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Sure it does.
You could also define it as chicken soup; as long as you provide the right axioms to deal with the value, it works.
You could make a calculus out of fruit if you wanted to. All that matters are the axioms and inference rules.
More to the point, for all the reasons already discussed it makes sense to define 0/0 (and expressions involving it) as 'not a number', to define it as a special value outside the number line. Heck, if it didn't make sense it wouldn't be used in every computer.
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mikedagr8
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Re: Hard: 24
« Reply #20 on: Aug 29th, 2007, 12:51am » |
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Quote:| In the future they'll have a way to define it. I'm already in that process and I'm 13. |
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If your honestly in the process, please share your thoughts, it'd be quite interesting to see how much I have changed since I was a 13 year old. 
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srn437
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Re: Hard: 24
« Reply #21 on: Aug 29th, 2007, 9:41am » |
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1/0 equals infinity(positive, negative, complex, or negacomplex). It can be simplified with 0 being replaced by +0, -0, +0(i), or -0(i). 0/0 can equal anything(but only one thing at a time). Also when in an equation it sometimes shifts value.
0/0=5
2(0)/0=10
0/0=10
(that doesn't make 5 equal to 10).
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Obob
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Re: Hard: 24
« Reply #22 on: Aug 29th, 2007, 10:06am » |
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The idea of defining 0/0 to be "anything, but only one thing at a time" does not prove to be very useful. Rather, it only further justifies why we do not define what 0/0 means.
So long as we are only working with real numbers, the expression 1/0 could possibly mean positive infinity or negative infinity, or neither. The idea of associating a value to 1/0 commonly arises in calculus, with the notion of a limit. So instead of talking about 1/0 directly, we would talk about 1/x, in the limit as x goes to 0 (or something like that). But 1/x as x goes to 0 could be either +infinity or -infinity, depending on if x approaches 0 through negative numbers or if x approaches 0 through positive numbers. So in this case we say that the limit does not exist, and do not define it. Similarly, the limit of 1/x^2 as x goes to 0 is indeed positive infinity, since it gets larger and larger whether x approaches 0 through positive numbers or through negative numbers.
The idea of a complex or negacomplex infinity is not useful at all, since either there should be a single infinity in the complex plane, or infinitely many of them. One construction of infinitely many infinities puts a single infinity in every direction from the origin of the complex plane. But by far the more common mathematical usage of infinity in complex arithmetic is that there is just a single infinity in the complex plane. An analogy is this: if we let a complex number z get closer and closer to zero in the complex plane, then 1/z goes farther and farther away from zero, but starts spinning around the origin like crazy. So there is no particular direction in which all the values are going, and we could not meaningfully assign a limit value if we were to put an infinity in every direction. But if we just have one infinity, we could in fact say that the limit is infinity: all the values are going farther and farther away from the origin, so they must be approaching the single point that is infinitely far off in the distance.
The reason that arithmetic involving division by zero is not usually defined is that it inherently leads to either contradictions or tons of special cases which don't actually make things simpler.
I suppose the moral of the story is that when it comes to simple arithmetic, if you weren't taught it in school then there is more likely than not a good reason.
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srn437
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Re: Hard: 24
« Reply #23 on: Aug 29th, 2007, 10:20am » |
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0 is positive, complex, negacomplex, and negative. Infinity in the case of 1/0 takes the reciprocal sign of 0(changed if you change 1 to another sign, which you multiply into infinity's sign).
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Obob
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Re: Hard: 24
« Reply #24 on: Aug 29th, 2007, 10:33am » |
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Thank you for reading my previous post and understanding the point...
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