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Topic: Pascal’s Triangle (Read 702 times) |
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Benny
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Pascal’s Triangle
« on: Sep 25th, 2009, 2:36pm » |
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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?
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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towr
wu::riddles Moderator
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Re: Pascal’s Triangle
« Reply #1 on: Sep 25th, 2009, 3:04pm » |
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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.
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| « Last Edit: Sep 25th, 2009, 3:10pm by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Grimbal
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Re: Pascal’s Triangle
« Reply #2 on: Sep 28th, 2009, 1:06am » |
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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 ...
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Benny
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Re: Pascal’s Triangle
« Reply #3 on: Sep 28th, 2009, 9:16am » |
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on Sep 28th, 2009, 1:06am, 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 ...
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I've just found a discussion of the problem here
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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.
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