I wondered this afternoon, and am now soliciting answers to, the following question: Given the 140 character limit on tweets and given the current (and presumable future) massive popularity of the service, how many years until every possible tweet has been tweeted?
Please state all assumptions relevant to your solution.
Overthinking my teaching 
I think every tweet will have been tweeted probably sooner than an infinite number of monkeys banging on an infinite number of typewriters, will accidentally reproduce a play by William Shakespeare.