Putting n=1 to 2000 in an excel sheet, I've noticed a pattern:
When n is odd, F(n)=(n+1)/2
When n is even, F(n)=-n/2
For question (1), if x=2011, and y=0, then F(x)=1006, F(y)=0, and F(x+y)=1006, for a total of 2012.
Furthermore, if we increase y by 2, then F(y) lowers by 1, and F(x+y) increases by 1.
Since we can do this indefinitely, and it leaves the total the same, the solution to part 1 is x=2011, and y=any even number (or vice versa).
For part (2), I can't find a solution, but I can't explain why there's no solution... Yet.
Posted by Dustin
on 2012-01-07 18:21:48