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How far off the edge of the table can we reach by stacking n identical blocks of length 1? A classical solution achieves an overhang of 1/2Hn, where Hn = Σni=1 1/i ~ ln n is the nth harmonic number, by stacking all the blocks one on top of another with the ith block from the top displaced by 1/2i beyond the block below. This solution is widely believed to be optimal. We show that it is exponentially far from optimal by giving explicit constructions with an overhang of Ω(n1/3). We also prove some upper bounds on the overhang that can be achieved. The stability of a given stack of blocks corresponds to the feasibility of a linear program and so can be efficiently determined.