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Inspired by various astrophysical phenomenons, it is suggested that pulsar-like compact stars are comprised entirely of strangeons (quark-clusters with three-light-flavor symmetry) and a small amount of electrons. In order to better constrain the properties of strangeon stars, we propose a linked bag model to describe the condensed matter by the strong interaction (i.e., strong condensed matter) in both 2-flavoured (nucleons) and 3-flavoured (hyperons, strangeons, etc.) scenarios. The model parameters are calibrated to reproduce the saturation properties of nuclear matter, which are later applied to hyperon matter and strangeon matter. Compared with baryon matter, the derived energy per baryon of strangeon matter is reduced if the strangeon carries a large number of valence quarks, which stiffens the equation of state and consequently increases the maximum mass of strangeon stars. In a large parameter space, the maximum mass and tidal deformability of strangeon stars predicted by the linked bag model are consistent with the current astrophysical constraints. It is found that the maximum mass of strangeon stars can be as large as $\sim 2.5M_\odot$, while the tidal deformability of a $1.4M_\odot$ strangeon star lies in the range of $180\lesssim Λ_{1.4} \lesssim 340$.