A correspondence called the double copy relates quantities in gauge and gravity theories, as well as a novel scalar theory with two types of colour charge (“biadjoint scalar theory”). It is not yet known whether the double copy is fully non-perturbative, and previous attempts to double copy nonperturbative solutions of biadjoint scalar theory have failed. In this talk, we look for Euclidean solutions of biadjoint scalar theory, hoping that they might be related to gauge / gravity instantons. Mysteriously, however, the simplest nonlinear Euclidean solutions vanish in precisely four spacetime dimensions. We resolve the puzzle as to why this happens, and comment on the implications for how to double copy instantons in general.