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ABSTRACT Accurate stellar parameters of stars in open clusters can help constrain models of stellar structure and evolution. Here, we wish to determine the age and metallicity content of the open cluster NGC 2506. To this end, we investigated three detached eclipsing binaries (DEBs; V2032, V4, and V5) for which we determined their masses and radii, as well as four red giant branch stars for which we determined their effective temperatures, surface gravities, and metallicities. Three of the stars in the DEBs have masses close to the cluster turn-off mass, allowing for extremely precise age determination. Comparing the values for the masses and radii of the binaries to BaSTI (a Bag of Stellar Tracks and Isochrones) isochrones, we estimated a cluster age of 2.01 ± 0.10 Gyr. This does depend on the models used in the comparison, where we have found that the inclusion of convective core-overshooting is necessary to properly model the cluster. From red giant branch stars, we determined values for the effective temperatures, the surface gravities, and the metallicities. From these we find a cluster metallicity of −0.36 ± 0.10 dex. Using this value and the values for the effective temperatures, we determine the reddening to be E(b − y) = 0.057 ± 0.004 mag. Furthermore, we derived the distance to the cluster from Gaia parallaxes and found 3.101 ± 0.017 kpc, and we have performed a radial velocity membership determination for stars in the field of the cluster. Finally, we report on the detection of oscillation signals in γ Dor and δ Scuti members in data from the Transiting Exoplanet Survey Satellite (TESS) mission, including the possible detection of solar-like oscillations in two of the red giants. 

Context. Models of stellar structure and evolution can be constrained using accurate measurements of the parameters of eclipsing binary members of open clusters. Multiple binary stars provide the means to tighten the constraints and, in turn, to improve the precision and accuracy of the age estimate of the host cluster. In the previous two papers of this series, we have demonstrated the use of measurements of multiple eclipsing binaries in the old open cluster NGC 6791 to set tighter constraints on the properties of stellar models than was previously possible, thereby improving both the accuracy and precision of the cluster age. Aims. We identify and measure the properties of a non-eclipsing cluster member, V56, in NGC 6791 and demonstrate how this provides additional model constraints that support and strengthen our previous findings. Methods. We analyse multi-epoch spectra of V56 from FLAMES in conjunction with the existing photometry and measurements of eclipsing binaries in NGC6971. Results. The parameters of the V56 components are found to be M p  = 1.103 ± 0.008  M ⊙ and M s  = 0.974 ± 0.007  M ⊙ , R p  = 1.764 ± 0.099  R ⊙ and R s  = 1.045 ± 0.057  R ⊙ , T eff,p  = 5447 ± 125 K and T eff,s  = 5552 ± 125 K, and surface [Fe/H] = +0.29 ± 0.06 assuming that they have the same abundance. Conclusions. The derived properties strengthen our previous best estimate of the cluster age of 8.3 ± 0.3 Gyr and the mass of stars on the lower red giant branch (RGB), which is M RGB  = 1.15 ± 0.02  M ⊙ for NGC 6791. These numbers therefore continue to serve as verification points for other methods of age and mass measures, such as asteroseismology.