Question: Problem 4 . (20 points) A partial Latin square of order n is an n x n array in which each entry is either empty

Problem 4 . (20 points) A partial Latin square of order n is an n x n array in which each entry is either empty or contains an element from [n] = {1, ,n). Each row and each column contains each element from [nl at most once. Colburn Q showed that the problem to decide whether a given partial Latin square can be completed to a Latin square is NP-complete. Given this fact, show that (a) the problem to decide whether a given n xn Futoshiki problem can be sol 8 is NP-complete (b) the problern to decide whether a given n2 x Sudoku problem. can solved is NP-complete

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