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Huisgen's 1960 announcement of the concept of 1,3‐dipolar cycloadditions was published the year before Alder's study of the reaction of diazomethane and dimethylfulvene. The diazomethane reaction was studied again in 1970 by Houk et al. and shown to give a [6+4] adduct. Padwa's nitrile ylide cycloaddition to dimethylfulvene (1978) gave [6+4] and [4+2] adducts. We performed computational studies of these reactions with density functional theory (DFT) and show that they involve ambimodal [6+4]/[4+2] transition states that can lead to either type of cycloadduct from one transition state. We dedicate this paper to the extraordinary life and humanity of Rolf Huisgen, and to the undying influence of his discoveries on chemistry. [ABSTRACT FROM AUTHOR]