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        riddles >> easy >> Number sequence
        
(Message started by: Thomson on Jan 13^th, 2005, 2:08pm)

Title: Number sequence
Post by Thomson on Jan 13^th, 2005, 2:08pm

What is the missing value in the following sequence?

2616, 3, 11, 10850, _____, 25, 2038

Title: Re: Number sequence
Post by THUDandBLUNDER on Jan 13^th, 2005, 10:27pm

Is it Easy?

Title: Re: Number sequence
Post by Thomson on Jan 14^th, 2005, 4:29pm

Easy-ish. But it's always like that when you have the answer. -_-

I'm not sure, maybe it could be medium or hard.

Title: Re: Number sequence
Post by puzzlecracker on Jan 14^th, 2005, 6:42pm

this problem doesnt have an answer... he just made it up. be serious please.

Title: Re: Number sequence
Post by THUDandBLUNDER on Jan 14^th, 2005, 9:25pm

on 01/14/05 at 18:42:10, 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'.

Title: Re: Number sequence
Post by puzzlecracker on Jan 14^th, 2005, 9:49pm

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

Title: Re: Number sequence
Post by TenaliRaman on Jan 15^th, 2005, 1:12am

on 01/14/05 at 21:49:38, 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.

Title: Re: Number sequence
Post by rmsgrey on Jan 15^th, 2005, 9:00am

Giving P(x_i) for N distinct x_i 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 x_i to be distinct guarantees non-degeneracy.