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?
(In reply to re(7): What now ? - you're right again !!
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