| Summary: | In this paper we define a bridge between pairings and colorings of the hypergraphs by introducing a generalization of pairs called t-cakes for t ∈ ℕ, t ≥ 2. For t = 2 the 2-cakes are the same as the well-known pairs of system of distinct representatives, that can be turned to pairing strategies in Maker-Breaker hypergraph games, see Hales and Jewett [12]. The two-colorings are the other extremity of t-cakes, in which the whole ground set of the hypergraph is one big cake that we divide into two parts (color classes). Starting from the pairings (2-cake placement) and two-colorings we define the generalized t-cake placements where we pair p elements by q elements (p, q ∈ ℕ, 1 ≤ p, q < t, p + q = t).
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