Pattern Decoder
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I need to figure out the formula/pattern/algorithm needed to convert the number on the left into a checksum on the right. Here are a few examples 6789542137 ; 53426 7274707623 ; 13890 7608909976 ; 21097 7866018419 ; 46204 8185833863 ; 59982 8052724826 ; 68535 Please help Thanks
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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
- 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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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
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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I need to figure out the formula/pattern/algorithm needed to convert the number on the left into a checksum on the right. Here are a few examples 6789542137 ; 53426 7274707623 ; 13890 7608909976 ; 21097 7866018419 ; 46204 8185833863 ; 59982 8052724826 ; 68535 Please help Thanks
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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- 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!!
The problem will arise with the seventh line of the sequence. :-D
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] -
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."
why is it assumed that f(n) = 0 for all other n
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I need to figure out the formula/pattern/algorithm needed to convert the number on the left into a checksum on the right. Here are a few examples 6789542137 ; 53426 7274707623 ; 13890 7608909976 ; 21097 7866018419 ; 46204 8185833863 ; 59982 8052724826 ; 68535 Please help Thanks
This question reminds me of the hollywood movie "Beautiful Mind".
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why is it assumed that f(n) = 0 for all other n
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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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."
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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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
f(100) = 10
f(81) = 9
f(64) = 8
f(49) = 7
f(36) = 6
f(25) = 5f(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] -
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
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 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."
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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f(100) = 10
f(81) = 9
f(64) = 8
f(49) = 7
f(36) = 6
f(25) = 5f(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]okay you can take any other example....this was just to prove the point....
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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
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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okay you can take any other example....this was just to prove the point....
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] -
- 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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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
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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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."
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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I need to figure out the formula/pattern/algorithm needed to convert the number on the left into a checksum on the right. Here are a few examples 6789542137 ; 53426 7274707623 ; 13890 7608909976 ; 21097 7866018419 ; 46204 8185833863 ; 59982 8052724826 ; 68535 Please help Thanks
You call the right-hand value a checksum. Why not assume that's what it really is? Checksums are performed on blocks of data, usually of a fixed size, in bit-wise fashion. That is, each character is loaded into a shift register, then the bits are shifted out and summed. Checksums originated with serial data communications, wherein a block of data was shifted out to the communications media and the bits summed as it was transmitted. The total of the checksum was tacked on to the end of each message and sent. At the receiving end the message was serially loaded into a register while the bits were summed. The total value of the sum was then compared to the last block of data sent, which was the checksum calculated by the sender. If they matched, the message was assumed good; if not, a NACK was returned to the sender, and the sender retransmitted. Convert your data into binary - an 8-bit character is probably acceptable, unless you assume Unicode was used. Pad the higher-order bits with zeroes and sum the bits. Convert the result back into decimal and look for the checksum. This method may take a while, as checksums were used on fixed block sizes and you don't know what size was used. Note, too, that this only applies to text data. Real numbers encoded using IEEE standards or other methods may convert differently. Without a lot more information about the problem domain it's impossible to suggest anything short of brute force decryption.
"A Journey of a Thousand Rest Stops Begins with a Single Movement"