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Please give us some hints, for instance: will this help to understand the origin of the Universe? 
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
[My articles]
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Can you supply any more information? A bunch of numbers and their checksum isn't much to go on...
"If only God would give me some clear sign! Like making a large deposit in my name in a Swiss bank."
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unfortunately that is all the information I have. What i am trying to do is find out what formula/algorithm when applied to the 10 digit number will get me the 3-5 digit code. Any help would be great
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hdsouza1 wrote: unfortunately that is all the information I have. What i am trying to do is find out what formula/algorithm when applied to the 10 digit number will get me the 3-5 digit code. Any help would be great
I'm afraid that's near-impossible. It's equivalent to trying to decrypt an encrypted message given no information about the encryption. You have to have some idea how it functions otherwise it could, quite literally, be among hundreds of thousands of possible algorithms. For all I know, these could be nothing but randomly generated numbers...
"If only God would give me some clear sign! Like making a large deposit in my name in a Swiss bank."
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Good luck.
"The clue train passed his station without stopping." - John Simmons / outlaw programmer
"Real programmers just throw a bunch of 1s and 0s at the computer to see what sticks" - Pete O'Hanlon
"Not only do you continue to babble nonsense, you can't even correctly remember the nonsense you babbled just minutes ago." - Rob Graham
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a * x ^ 6 + b * x ^ 5 + c * x ^4 + d * x ^ 3 + e * x ^ 2 + f * x = y
use you data you can solute a、b、c、d、e、f.
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Hi Shrewdlin, Thanks for your reply. Need a little more help. What is
1) x and y
2) Does x^5 mean x to the power of 5
Thanks
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1) x and y is variable
2) yes, it means x to the power of 5
yan can use your data to make six equation for example:
a * 6789542137 ^ 6 + b * 6789542137 ^ 5 + c * 6789542137 ^ 4 + d * 6789542137 ^3 + d * 6789542137 ^ 2 + f * 6789542137 = 53426 (this is the first one, you can do the other)
six equation to solve six variable can you calculate the a、b、c、d、e、f
then use the known a、b、c、d、e、f to rebuild the equation
the data is very big you can use maple software for you!!!good luck!!
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The problem will arise with the seventh line of the sequence.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
[My articles]
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Hi Shrewdlin,
Thanks for the detailed explanation. I guess I will have to buy the maple software. before I buy I was wondering how you got to this formula. Did you run the numbers through some program of yours to get this formula
Thanks
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You can solve it in a spreadsheet, for the theory see Polynomial Interpolation[^], but unless you know that the answer you are looking for is a polynomial it is almost certainly wrong.
A 5th order polynomial can be fitted to your data:
a * x ^ 5 + b * x ^ 4 + c * x ^3 + d * x ^ 2 + e * x ^ 1 + f = y
but so can a 6th
a * x ^ 6 + b * x ^ 4 + c * x ^3 + d * x ^ 2 + e * x ^ 1 + f = y
a 7th
a * x ^ 7 + b * x ^ 4 + c * x ^3 + d * x ^ 2 + e * x ^ 1 + f = y
or a different 7th
a * x ^ 7 + b * x ^ 6 + c * x ^3 + d * x ^ 2 + e * x ^ 1 + f = y
or a Fourier series
a * sin(x) + b * sin(2*x) + c * sin(3*x) + d * sin(4*x) + e * sin(5*x) + f = y
or basically a linear combination of any collection of 6 functions (some collections of 6 functions will fail, but most will succeed). There are also a wide range of possible solutions that don't fall into these categories.
So unless you can state why any of the above solutions should or shouldn't be the one you are looking for, you don't know enough about the problem to solve it.
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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Wait! Don't buy Maple! You need to tell us something about what you expect out of this "decoder". If you just want any function that will match up at these points, sure, the polynomial will work but it will go crazy outside of these points. I'm assuming you're trying to "reproduce" some other function which spat out these values, in which case the polynomial is pretty much guaranteed to be the wrong thing. On the other hand, if you're just looking for a rule that takes on those values, you can use the function which takes on those specific values at those specific points and is zero everywhere else. It's about as likely as the polynomial and you don't have to buy Maple to compute it.
In general, if you are trying to reproduce the function that somebody else carefully chose to produce these values you're probably out of luck. There are an infinite number of functions that will do that. If you're looking for any function at all, then either take the one I mentioned above or explain whatever other details you've got that keep that one from working. You see these sort of questions in "brainteasers" where you have a chance of solving them, but if this was designed to prevent cracking, you're not likely to chance across the right answer.
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The question as you have posed it is nonsense. There are an infinite number of solutions. For example, I guess this is not useful, but the formula f(n) defined by:
f(6789542137) = 53426
f(7274707623) = 13890
f(7608909976) = 21097
f(7866018419) = 46204
f(8185833863) = 59982
f(8052724826) = 68535
f(n) = 0 for all other n
actually answers your question.
Perhaps you could explain what you are trying to do?
Peter
"Until the invention of the computer, the machine gun was the device that enabled humans to make the most mistakes in the smallest amount of time."
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why is it assumed that f(n) = 0 for all other n
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Because based on the finite sample population he posted, it is a valid assumption.
"If only God would give me some clear sign! Like making a large deposit in my name in a Swiss bank."
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But he has just given you few samples of input and output of a function.
all the remaining output cannot be assumed to be zero
what you are saying is this:
if i say
f(100) = 10
f(81) = 9
f(64) = 8
f(49) = 7
f(36) = 6
f(25) = 5
here its a simple example in which output is just square root of input
now based on your assumption
f(n) = 0, does that mean square root of all remaining numbers are zero
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f(100) = 10
f(81) = 9
f(64) = 8
f(49) = 7
f(36) = 6
f(25) = 5
f(n) = 0 for all other n values
It is a perfect legal (and admittely beautiful) function. It satisfies all your requirements until you don't specify the 'square root' one.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
[My articles]
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okay you can take any other example....this was just to prove the point....
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You didn't prove the point and without further requirements the OP's request is pointless.
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler.
-- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong.
-- Iain Clarke
[My articles]
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He provides a finite sample of 6 data points. The function he provided describes them perfectly. If the sample size is 6, then all others must be zero. There's nothing wrong with it and it's a perfect fit to the data.
"If only God would give me some clear sign! Like making a large deposit in my name in a Swiss bank."
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he never says the sample size is 6 he just gave you 6 to you because he cannot go on posting all samples
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Cosmic Egg wrote: he never says the sample size is 6 he just gave you 6 to you because he cannot go on posting all samples
...and the function fits the finite sample. The function fits the observed data: any other (unknown) points are irrelevant and can therefore be set to zero. Adding additional points will change the function, obviously, so that if f(7) were defined, then setting f(n>7) = 0 would fit the new data.
"If only God would give me some clear sign! Like making a large deposit in my name in a Swiss bank."
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73Zeppelin wrote: If the sample size is 6, then all others must be zero
That's extraordinarily poor logic. There are six known values; that's no reason to extrapolate all other values to zero. It just means we only know 6 of them; unless a pattern can be derived from the known samples, we know nothing about the other possible values.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"
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Roger Wright wrote: That's extraordinarily poor logic. There are six known values; that's no reason to extrapolate all other values to zero. It just means we only know 6 of them; unless a pattern can be derived from the known samples, we know nothing about the other possible values.
It's a discretization of the available data. If he's trying to fit six observations of the sample population, then setting the remaining data to zero is completely acceptable. That's not to say we assume the rest of the data is zero, but that we are fitting only to the points that we know.
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This question reminds me of the hollywood movie "Beautiful Mind".
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