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The mathematical structure of sudoku is like "hard constraint satisfaction problems".

constraint satiscaction problems are defined as sets of objects whose state must satisfy a number of limitations
 very broad, but the eight queens puzzle is another example, the map 4colouring problem from Math 239 is another example
 Sudoku is one of Karp's 21 NPcomplete problems for N x N grids
 it is called an exact cover type problem
 exact cover in math just means that for a set S of subsets of set X, we want to find a subset of S, S * that contains every element in X exactly once
 exact cover problem is a decision problem and is NPcomplete

Boolean Satisfiability Problem (SAT) tries to find out whether a boolean expression is satisifiable (some possible combination of variables s.t. the expression is TRUE)
 first proven NPcomplete problem
TODO