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We present the results of a photometric variability survey in the young open cluster Stock 14 and the surrounding fields. In total, we detected 103 variable stars of which 88 are new discoveries. We confirm short-period, low-amplitude light variation s in two eclipsing members of the cluster, HD 101838 and HD 101794. In addition, we find two new beta Cephei stars of which one, HD 101993, is also a member. The sample of pulsating cluster members is supplemented by one multimode slowly pulsating B-type star and several single-mode candidates of this type. The other pulsating stars in our sample are mostly field stars. In particular, we found fourteen delta Scuti stars including one gamma Dor/delta Sct hybrid pulsator. From our UBV photometry we derived new parameters of Stock 14: the mean reddening E(B-V) = 0.21 +/- 0.02 mag, the true distance modulus, 11.90 +/- 0.05 mag, and the age, 20 +/- 10 Myr. Finally, we use the new photometry to analyze changes of the 6.322-d orbital period of the bright eclipsing binary and the member of the cluster, V346 Cen. In addition to the known apsidal motion, we find that another effect, possibly light-time effect in a hierarchical system of a very long orbital period, affects these changes. The updated value of the period of apsidal motion for this system amounts to 306 +/- 4 yr. The open cluster Stock 14 was found to be a fairly good candidate for successful ensemble asteroseismology.
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