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Circle of numbers (Posted on 2005-05-27) Difficulty: 2 of 5
Over 2000 numbers are around a circle. Each number is the sum of its left and right neighbors.

Given that one of the numbers is a one, how many numbers (as a minimum) must there be?

See The Solution Submitted by McWorter    
Rating: 3.7500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(8): What now ? - you're right again !! | Comment 24 of 31 |
(In reply to re(7): What now ? - you're right again !! by McWorter)

Charlie proved that the largest string of numbers you can write whithout falling into a cycle is 6. In other words, you NEED to repeat your numbers in blocks of 6 or smaller.

At the same time, from his proof one can see that any smaller block must contain all 0's.

Therefore, as other's have said, the solution must be 2004. This solution holds true as long as any number other than 0 appears in the circle (in general, you could have said "Given that at least one of the numbers in the circle is not 0..." instead of mentioning the  particular number 1).
  Posted by ajosin on 2005-06-02 13:50:10

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