Source: Australian Mathematical Society Gazette Puzzle Corner
Problem: An optimist and a pessimist are examining a sequence of numbers. The optimist remarks, ‘Oh jolly! The sum of any eight consecutive terms is positive!’ But the pessimist interjects, ‘Not so fast, the sum of any five consecutive terms is negative.’ Can they both be right? How long can this sequence of numbers be?
Incentive: Treat at H8 Canteen/Sodexho Cafeteria for the first person to solve it :P
Update (27/07/10): Solution: Posted in comments by Varun Jog (Berkeley Grad Student, EE IITB Alumnus) and Siddhant Agarwal (EE Senior Undergraduate, IITB)