Puzzle Challenge Site
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Problem in question: You may solve this problem with or without programming, but it has been optimised for solution with a programming method. The Fibonacci sequence of numbers is defined as:
F[0]=0 F[1]=1 and for all x>1, F[x]=F[x-1]+F[x-2]PLEASE do not post the answer.What is the smallest value of x>0 such that F[x]=0 mod 2^32PLEASE do not post the answer. I never thought I'd revert to posting here to get help with this question from a Puzzel Challange Site[^]. The history behind it, I've been stuck on this for a year. Not a solid year but off and on. I've written a LongMath Class[^] to help me solve it but I still haven't found the the answer. I've read through the posts on the challange site and they're talk'n about, "If you understand the Fibonacci sequence you won't need a program to figure it out. I'm looking for help in solving the problem on my own. The site is older and not alot of visitors to the forums. I've applied my LonMath Class to a sandbox app to help solve it but I'm not sure if I'm performing F[x]=0 mod 2^32 correctly. Fibonacci Pilot[^]I'm listening but I only speak GEEK.
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Problem in question: You may solve this problem with or without programming, but it has been optimised for solution with a programming method. The Fibonacci sequence of numbers is defined as:
F[0]=0 F[1]=1 and for all x>1, F[x]=F[x-1]+F[x-2]PLEASE do not post the answer.What is the smallest value of x>0 such that F[x]=0 mod 2^32PLEASE do not post the answer. I never thought I'd revert to posting here to get help with this question from a Puzzel Challange Site[^]. The history behind it, I've been stuck on this for a year. Not a solid year but off and on. I've written a LongMath Class[^] to help me solve it but I still haven't found the the answer. I've read through the posts on the challange site and they're talk'n about, "If you understand the Fibonacci sequence you won't need a program to figure it out. I'm looking for help in solving the problem on my own. The site is older and not alot of visitors to the forums. I've applied my LonMath Class to a sandbox app to help solve it but I'm not sure if I'm performing F[x]=0 mod 2^32 correctly. Fibonacci Pilot[^]I'm listening but I only speak GEEK.
I'm intrigued, but I'm not about to log on to that site, is that the full text of the puzzle? I ask because it seems to me that
0 mod 2^32equals 0; so, as stated, the puzzle has no solution. -
I'm intrigued, but I'm not about to log on to that site, is that the full text of the puzzle? I ask because it seems to me that
0 mod 2^32equals 0; so, as stated, the puzzle has no solution.Nono, in real life as well as in maths, numbers have no upper bound and no limit as to the number of bits; so there might well be non-zero Fibonnacci numbers that take a divisor of 2^32. In fact, I can assure you there are infinitely many solutions to this one, and the smallest of them can be calculated with a simple calculator ! The puzzle site is very challenging, and yes, most often the problem descriptions are short, and sometimes very ... puzzling. :)
Luc Pattyn
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Problem in question: You may solve this problem with or without programming, but it has been optimised for solution with a programming method. The Fibonacci sequence of numbers is defined as:
F[0]=0 F[1]=1 and for all x>1, F[x]=F[x-1]+F[x-2]PLEASE do not post the answer.What is the smallest value of x>0 such that F[x]=0 mod 2^32PLEASE do not post the answer. I never thought I'd revert to posting here to get help with this question from a Puzzel Challange Site[^]. The history behind it, I've been stuck on this for a year. Not a solid year but off and on. I've written a LongMath Class[^] to help me solve it but I still haven't found the the answer. I've read through the posts on the challange site and they're talk'n about, "If you understand the Fibonacci sequence you won't need a program to figure it out. I'm looking for help in solving the problem on my own. The site is older and not alot of visitors to the forums. I've applied my LonMath Class to a sandbox app to help solve it but I'm not sure if I'm performing F[x]=0 mod 2^32 correctly. Fibonacci Pilot[^]I'm listening but I only speak GEEK.
Hi, there are several bulletin boards on the caesum site, there is one per level, and one per problem (only accessible once you solved it!). The fibber problem can be cracked easily by programming; there are tsraightforward ways, and even better ones. It can also be solved by hand using a simple calculator (hint: scan the Fibonacci sequence looking for a pattern in the powers of 2). :)
Luc Pattyn
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Nono, in real life as well as in maths, numbers have no upper bound and no limit as to the number of bits; so there might well be non-zero Fibonnacci numbers that take a divisor of 2^32. In fact, I can assure you there are infinitely many solutions to this one, and the smallest of them can be calculated with a simple calculator ! The puzzle site is very challenging, and yes, most often the problem descriptions are short, and sometimes very ... puzzling. :)
Luc Pattyn
Yes, but as stated, we're not dividing (or MODing) the xth Fibonnacci number by 2^32, but comparing it with
0 mod 2^32which ought to be 0; isn't 0 mod anything (except 0) always 0? So themod 2^32is unnecessary. That simplifies the puzzle toF[x]=0, but that's only true when x=0, and the puzzle is to find a solution wherex>0, that's why I see no solution. Certainly, if the puzzle statedmod 2^32 = 0, then I would understand it. -
Yes, but as stated, we're not dividing (or MODing) the xth Fibonnacci number by 2^32, but comparing it with
0 mod 2^32which ought to be 0; isn't 0 mod anything (except 0) always 0? So themod 2^32is unnecessary. That simplifies the puzzle toF[x]=0, but that's only true when x=0, and the puzzle is to find a solution wherex>0, that's why I see no solution. Certainly, if the puzzle statedmod 2^32 = 0, then I would understand it.mathematician use a lot of different notations for modulo arithmetic. All of the following are equivalent: a ≡ b (mod M) a = b (mod M) a ≡ b mod M a = b mod M and they all actually mean: a % M = b % M so the modulo operator is often mentioned only once, and sometimes not at all (but just implied by text or context) Therefore the problem at hand is really asking for the first Fibonacci number that is a multiple of 2^32. Of course, a more programmer-friendly notation would have been: find x such that F(x) mod 2^32 = 0 instead of: F(x) = 0 mod 2^32 :)
Luc Pattyn
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mathematician use a lot of different notations for modulo arithmetic. All of the following are equivalent: a ≡ b (mod M) a = b (mod M) a ≡ b mod M a = b mod M and they all actually mean: a % M = b % M so the modulo operator is often mentioned only once, and sometimes not at all (but just implied by text or context) Therefore the problem at hand is really asking for the first Fibonacci number that is a multiple of 2^32. Of course, a more programmer-friendly notation would have been: find x such that F(x) mod 2^32 = 0 instead of: F(x) = 0 mod 2^32 :)
Luc Pattyn
Aside: Well, if
a = b mod Mmeansa % M = b % Mhow would I expressa = b % M? -
Aside: Well, if
a = b mod Mmeansa % M = b % Mhow would I expressa = b % M?Program statements must be accurate and unambiguous; thats what compilers need, and programmers must provide. Mathematical equations must also be accurate and unambiguous. However math publications try to come up with the clearest and/or shortest notation, often at the expence of some ambiguity (which then should be resolved by adding a textual description of the local conventions, if necessary). It is important to recognize which is which. On most of the CP message boards, there is no doubt, it is code in one of the many standard programming languages. On the Maths and Algos board, some of it is math equations, and must be treated as such. ;)
Luc Pattyn
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mathematician use a lot of different notations for modulo arithmetic. All of the following are equivalent: a ≡ b (mod M) a = b (mod M) a ≡ b mod M a = b mod M and they all actually mean: a % M = b % M so the modulo operator is often mentioned only once, and sometimes not at all (but just implied by text or context) Therefore the problem at hand is really asking for the first Fibonacci number that is a multiple of 2^32. Of course, a more programmer-friendly notation would have been: find x such that F(x) mod 2^32 = 0 instead of: F(x) = 0 mod 2^32 :)
Luc Pattyn
Luc Pattyn wrote:
find x such that F(x) mod 2^32 = 0
Your correct that the author mentions that the above equation is another way to look at it. Thank you for the help in this puzzle. I've been reviewing the series for a pattern of numbers that follow a power of 2, but I'm not much of a mathematician.
I'm listening but I only speak GEEK.
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Hi, there are several bulletin boards on the caesum site, there is one per level, and one per problem (only accessible once you solved it!). The fibber problem can be cracked easily by programming; there are tsraightforward ways, and even better ones. It can also be solved by hand using a simple calculator (hint: scan the Fibonacci sequence looking for a pattern in the powers of 2). :)
Luc Pattyn
I've been running the squence and squaring each number looking for an noticable pattern but I'm not seeing anything. Most of the puzzles I've run into have an underlying reson for the puzzle. Would you know where else this information would be used? Why would I be looking at a pattern of squared numbers?
I'm listening but I only speak GEEK.
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I've been running the squence and squaring each number looking for an noticable pattern but I'm not seeing anything. Most of the puzzles I've run into have an underlying reson for the puzzle. Would you know where else this information would be used? Why would I be looking at a pattern of squared numbers?
I'm listening but I only speak GEEK.
Squaring ?? :confused: Just look at the Fib numbers in binary...
Luc Pattyn
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Squaring ?? :confused: Just look at the Fib numbers in binary...
Luc Pattyn
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Luc Pattyn wrote:
find x such that F(x) mod 2^32 = 0
Your correct that the author mentions that the above equation is another way to look at it. Thank you for the help in this puzzle. I've been reviewing the series for a pattern of numbers that follow a power of 2, but I'm not much of a mathematician.
I'm listening but I only speak GEEK.
That would be why I asked if you could post the full actual text of the puzzle.
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Problem in question: You may solve this problem with or without programming, but it has been optimised for solution with a programming method. The Fibonacci sequence of numbers is defined as:
F[0]=0 F[1]=1 and for all x>1, F[x]=F[x-1]+F[x-2]PLEASE do not post the answer.What is the smallest value of x>0 such that F[x]=0 mod 2^32PLEASE do not post the answer. I never thought I'd revert to posting here to get help with this question from a Puzzel Challange Site[^]. The history behind it, I've been stuck on this for a year. Not a solid year but off and on. I've written a LongMath Class[^] to help me solve it but I still haven't found the the answer. I've read through the posts on the challange site and they're talk'n about, "If you understand the Fibonacci sequence you won't need a program to figure it out. I'm looking for help in solving the problem on my own. The site is older and not alot of visitors to the forums. I've applied my LonMath Class to a sandbox app to help solve it but I'm not sure if I'm performing F[x]=0 mod 2^32 correctly. Fibonacci Pilot[^]I'm listening but I only speak GEEK.
Take a look at http://mathworld.wolfram.com/FibonacciNumber.html[^] Particularly the paragraph just below the big triangle.