Source: IITM Friend (who did not want his name to be disclosed). Also read it once in CLR (Introduction to Algorithms)
Given an array of n numbers. Finding minimum takes n-1 comparisons. Finding maximum takes n-1 comparisons. If you had to simultaneously find both minimum and maximum, can you do it in less than 2n-2 comparisons?
Update (11/12/09): Solution by Ameya and Me in comments !!