We solve the shadow problem in the n-dimensional Euclidean space \( {\mathbb{N}}^n \) for a family of sets obtained from any convex domain with nonempty interior with the help of parallel translations and homotheties. Moreover, we determine the number of balls with centers on the sphere sufficient for making a shadow in the n-dimensional complex (hypercomplex) space.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 757–762, June, 2016.
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Zelins’kyi, Y.B., Stefanchuk, M.V. Generalizations of the Shadow Problem. Ukr Math J 68, 862–867 (2016). https://doi.org/10.1007/s11253-016-1262-x
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DOI: https://doi.org/10.1007/s11253-016-1262-x