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Form Finding From Solution (Posted on 2016-09-05) Difficulty: 3 of 5
Consider the equation:
P1* P2 + P2* P3+…..+ Pn-1* Pn + Pn* P1 = 0, where n is a positive integer, and each Pi= 1 or -1

Derive the general form of n such that the above equation has at least one valid solution.

No Solution Yet Submitted by K Sengupta    
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re: seems to be a solution Comment 2 of 2 |
(In reply to seems to be a solution by Charlie)

For any multiple of 4, say n=4*k, repeat the string {1,1,-1,-1} k times.  Then the products in the sum alternate 1,-1,1,-1... with an even number of terms, 2*k each of 1 and -1.  The sum of these must be 0.  This proves all multiples of 4 have at least one valid equaiton.
  Posted by Brian Smith on 2016-09-05 12:56:31

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