Several abundance analyses of Galactic open clusters (OCs) have shown a tendency for Ba but not for other heavy elements (La-Sm) to increase sharply with decreasing age such that Ba was claimed to reach [Ba/Fe] ≃ +0.6 in the youngest clusters (ages < 100 Myr) rising from [Ba/Fe] = 0.00 dex in solar-age clusters. Within the formulation of the s-process, the difficulty to replicate higher Ba abundance and normal La-Sm abundances in young clusters is known as the barium puzzle. Here, we investigate the barium puzzle using extremely high-resolution and high signal-to-noise spectra of 24 solar twins and measured the heavy elements Ba, La, Ce, Nd, and Sm with a precision of 0.03 dex. We demonstrate that the enhanced Ba II relative to La-Sm seen among solar twins, stellar associations, and OCs at young ages (<100 Myr) is unrelated to aspects of stellar nucleosynthesis but has resulted from overestimation of Ba by standard methods of LTE abundance analysis in which the microturbulence derived from the Fe lines formed deep in the photosphere is insufficient to represent the true line broadening imposed on Ba II lines by the upper photospheric layers from where the Ba II lines emerge. Because the young stars have relatively active photospheres, Ba overabundances most likely result from the adoption of a too low value of microturbulence in the spectrum synthesis of the strong Ba II lines but the change of microturbulence in the upper photosphere has only a minor affect on La-Sm abundances measured from the weak lines.