The search for the asymptotics of the Ramsey function R(3,k) has a long and fascinating history. It begins in the hill country surrounding Budapest and winding over the decades through Europe, America, Korea and Rio de Janiero. We explore it through a CS lens, giving algorithms that provide the various upper and lower bounds. The arguments are various more or less sophisticated uses of Erdos Magic and, indeed, many of the most important advances in the Probabilistic Method have come from these investigations.

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