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        riddles >> general problem-solving / chatting / whatever >> Pascal’s Triangle
        
(Message started by: BenVitale on Sep 25^th, 2009, 2:36pm)

Title: Pascal’s Triangle
Post by BenVitale on Sep 25^th, 2009, 2:36pm

Is there a way to determine how many odd elements there are in a particular row?

If we know how many there are in the n-th row can we predict for the (n+1)-th row?

Title: Re: Pascal’s Triangle
Post by towr on Sep 25^th, 2009, 3:04pm

Try drawing pascal's triangle modulo 2 and see if you notice anything. After a 16 or 32 rows or so it should be apparent. If you don't see anything by that time, draw lines through the 1s.

Title: Re: Pascal’s Triangle
Post by Grimbal on Sep 28^th, 2009, 1:06am

Or just compute the sequence and see if you notice a pattern:
1 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 ...

Title: Re: Pascal’s Triangle
Post by BenVitale on Sep 28^th, 2009, 9:16am

on 09/28/09 at 01:06:58, Grimbal wrote:

Or just compute the sequence and see if you notice a pattern:
1 2 2 4 2 4 4 8 2 4 4 8 4 8 8 16 2 4 4 8 ...

I've just found a discussion of the problem here (http://everything2.com/title/Pascal%2527s+triangle)

Quote:

An interesting problem is to determine the number of odd coefficients in the expansion of (x+y)ⁿ. Essentially, this reduces to determining the number of odd values in the n-th row of Pascal's Triangle.

Title: Re: Pascal’s Triangle
Post by towr on Sep 28^th, 2009, 10:00am

http://www.research.att.com/~njas/sequences/A001316