I attended an interesting seminar on the block stacking problem today given by Professor Mike Paterson of the University of Warwick.
Like all good problems, it can be stated simply: how far can a stack of *n* identical blocks be made to hang over the edge of a table?
The answer was widely believed to be of order log n (like the white shaded example above), but Mike Paterson and Uri Zwick previously constructed overhangs of order n^{1/3}.
In the seminar today, Paterson and his co-authors presented their proof that order *n^{1/3}* is indeed the upper bound possible, resolving a long-standing mathematical problem. Professor Paterson is an excellent orator, highly recommended.
Any idea if he's giving the presentation again at/around Warwick?
You must have specified the problem wrongly, because as you have stated it the answer is as far as you want.
@Odd_Bloke: No, sorry. These things tend to end up on department events pages quite early though - try looking there.
@Nick: Not if the answer is expressed as a function of n.
True for the case with multi-block layers.
In the classical, one block per layer case <a href="http://develop…" title="The Book Stacking Problem - Wikipedia and Mathworld Got It Wrong" rel="nofollow">this bloag</a> says the Wikipedia and Mathworld article are wrong...!