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An intercalate in a Latin square is a 2×2 Latin subsquare. Let N be the number of intercalates in a uniformly random n× n Latin square. We prove that asymptotically almost surely N>(1-o(1)) n^2/4, and that EN<(1+o(1)) n^2/2 (therefore asymptotically almost surely N< fn^2 for any f→∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problemarXiv:1607.04981v2 fatcat:e2fsicvtwfgrzctn6v7tzsglrq