You have 55 matches arranged in some number of piles of different sizes. You now do the following operation: pick one match from each pile, and form a new pile. You repeat this ad infinitum. What is the steady state? Is it unique?
Answer is intuitive :) Cheers!
Update (15th Feb 2012):
Assume steady state exists and try to solve the problem.
A much difficult version: Prove that steady state always exists.
Solution posted by Avradeep Bhowmik (aletterdoesnotblush), Sumanth Puram (IITM Alumnus, Engineer at Netapp), Mayur Agrawal (Agmay, IIT KGP Alumnus, PhD Student at Purdue University) in comments!
The difficult version posed by Nishant Totla (CSE IITB Senior Undergraduate) and solved by Gaurav Sinha (chera, IITK 1996 Graduate, Indian Revenue Service). Thanks a ton!