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   Author  Topic: Number sequence  (Read 712 times)
Thomson
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Number sequence  
« on: Jan 13th, 2005, 2:08pm »
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What is the missing value in the following sequence?
 
2616, 3, 11, 10850, _____, 25, 2038  
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ThudnBlunder
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Re: Number sequence  
« Reply #1 on: Jan 13th, 2005, 10:27pm »
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Is it Easy?
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Thomson
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Re: Number sequence  
« Reply #2 on: Jan 14th, 2005, 4:29pm »
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Easy-ish. But it's always like that when you have the answer. -_-
 
I'm not sure, maybe it could be medium or hard.
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puzzlecracker
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Re: Number sequence  
« Reply #3 on: Jan 14th, 2005, 6:42pm »
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this problem doesnt have an answer... he just made it up.  be serious please.
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Re: Number sequence  
« Reply #4 on: Jan 14th, 2005, 9:25pm »
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on Jan 14th, 2005, 6:42pm, puzzlecracker wrote:
this problem doesnt have an answer... he just made it up.  

So we can just make up an appropriate polynomial to fit the data and find the missing 'value'.
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Re: Number sequence  
« Reply #5 on: Jan 14th, 2005, 9:49pm »
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can you really do that?  although the probability is definitely on your side, for he seem not to use primarily prime numbers.. but that interesting
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Re: Number sequence  
« Reply #6 on: Jan 15th, 2005, 1:12am »
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on Jan 14th, 2005, 9:49pm, puzzlecracker wrote:
can you really do that?  although the probability is definitely on your side, for he seem not to use primarily prime numbers.. but that interesting

 
Yes definitely. Simply construct the difference table to find the missing value. For finding the polynomial, one can use the Newton's Interpolation Formula.
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Re: Number sequence  
« Reply #7 on: Jan 15th, 2005, 9:00am »
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Giving P(xi) for N distinct xi always defines precisely one polynomial P(x) of degree N-1 or less. You get N equations in N unknowns (the coeffecients of the polynomial), and requiring the xi to be distinct guarantees non-degeneracy.
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